CN105629733A - Fractional order cell neural network adaptive synchronization control and circuit design method - Google Patents
Fractional order cell neural network adaptive synchronization control and circuit design method Download PDFInfo
- Publication number
- CN105629733A CN105629733A CN201610065857.0A CN201610065857A CN105629733A CN 105629733 A CN105629733 A CN 105629733A CN 201610065857 A CN201610065857 A CN 201610065857A CN 105629733 A CN105629733 A CN 105629733A
- Authority
- CN
- China
- Prior art keywords
- formula
- fractional order
- circuit
- neural network
- design
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Landscapes
- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a fractional order cell neural network adaptive synchronization control and circuit design method. A fractional differential algorithm is selected, and the definition of a cell neural network equation is combined, thereby constructing a three-dimensional cell neural network system. The method comprises the steps: designing a drive-response system with a known drive system nonlinear parameter and an unknown response system nonlinear parameter based on the above system, constructing a new adaptive synchronizing controller and a parameter adaptive adjustment rate, and achieving the synchronization of the drive and response systems in numerical simulation; designing the circuit diagrams of the drive and response systems of the fractional order cell neural network, and achieving the circuit simulation of the controller and the adaptive adjustment rate. A simulation result indicates that the circuit simulation and the numerical simulation have the similar synchronous phase diagram, and the method verifies the accuracy of system theoretical analysis and the actual physical realizability. Therefore, the method is practical in the field of engineering.
Description
Technical field
The invention belongs to non-thread line chaotic circuit system field, relate to cell neural network, Synchronization Control theory and fractional order circuit thought.
Background technology
Chaos be the discovery that one of the greatest discovery in physics after the Theory of Relativity and quantum mechanics of 20th century, chaotic motion is the forms of motion that a kind of deterministic nonlinear system is exclusive, and showing as and being seen as finite motion in terms of local angle from global scope is then irregular motion. The feature of chaos is its extreme sensitivity to disturbance, and namely two chaos systems are from the initial condition of minute differences, through regular hour meeting rapid divergence, ultimately results in movement locus entirely different. Just because of the height random of chaotic signal, unpredictability, high complexity, and the being easily achieved property of definitiveness equation so that it is have bigger researching value and tempting application prospect thereof in engineering. Cell neural network (CellularNeuralNetworks, CNN) it is a kind of parallel computation phantom similar to human nerve's network, local connectivity matter is simply prone to ultra-large circuit (VLSI) and realizes, and can produce nonlinear kinetics chaos phenomenon even hyperchaos complex behavior. Cell neural network prediction science, image procossing, pattern recognition, secret communication, logic array computer structure etc. in have been achieved for developing widely. And Control of Chaotic Synchronization has become as one of current study hotspot as the key link of chaos applications, therefore the Synchronization Control research of dynamic stability is had realistic meaning and practical value by dynamic stability no less important by it.
Since nineteen ninety L.M.Pecora and T.L.Carrol proposes the thought of Chaotic Synchronous, the research of Chaotic Synchronous obtains flourish. The synchronous method occurred at present has: drive response method, active-passive method, control observation device method, active control, one way coupled map, adaptive synchronization method etc. Most synchronization scenario is all based on realizing on basis that system structure and parameter are all accurately understood, but in fact, it is difficult to accurately obtain systematic parameter by externally measured, even if some system its structure and parameter already known, interference due to external disturbance and noise, it is also difficult to the parameter making two chaos systems is identical.
Fractional calculus and integer rank calculus almost have same long developing history, and integer rank calculus is the special case of fractional calculus, and integer level system is that the idealization to actual chaos system processes. For in practical engineering application, the feature of new fractional-order system and structure are closer to reality, along with the development of fractional calculus, the Synchronization Control of chaotic systems with fractional order has more prominent using value and development prospect than the Synchronization Control of integer rank chaos system in fields such as secret communication, system controls. Up to now numerous research is compared in the Synchronization Control concentrating on integer rank chaos system, utilizes fractional order to realize cell neural network Self-adaptive synchronization control and parameter identification but rarely has report.
Up to now, although numerous scholars are for the dynamic characteristic of cell neural network, dynamic behavior and various engineer applied etc. have more thesis and work to deliver, such as cell neural network is based on the Equilibrium point of threshold stimulus function, airbound target identification based on cell neural network, the application etc. in License Plate of the memristor cell neural network, but these researchs are substantially based on the cell neural network on integer rank. Since fractional order theory proposes, chaotic systems with fractional order has had bigger development, the research of the such as Complete Synchronization of fractional order Chen chaos system and reverse sync, fractional order Liu chaos system and Experiment of Electrical Circuits thereof and control, fractional order Lorenz hyperchaotic system and circuit simulation thereof etc., but the cell neural network chaos system based on fractional order is studied seldom, utilizes fractional order to realize cell neural network Self-adaptive synchronization control and parameter identification rarely has report especially. But fractional calculus can describe the various dynamicss of real world and the actual physics phenomenon of system more accurately. Therefore the Synchronization Control research of fractional order is had to important theoretical research value and application prospect.
Summary of the invention
The present invention, on the basis of comprehensive cell neural network and the respective advantage of fractional order circuit, have devised a new fractional order cell neural network Circuits System. And utilize one drive system nonlinear parameter of this system constructing known and the drive response system of responding system nonlinear parameter value the unknown, realize this drive response system synchronization by Adaptive synchronization controller and regulation. Owing to its fractional order characteristic is closer to reality physical significance, therefore it has important actual value.
The present invention is achieved through the following technical solutions.
Step (1): according to cytocidal action lattice basic model, design integer rank three-dimensional cell nerve network system, and make system have chaotic characteristic by adjusting parameter.
Step (2): select fractional order differential definition and algorithm.
Step (3): build fractional order synchronous control system model.
Step (4): the integer rank three-dimensional cell neutral net built based on step (1), theoretical in combination with step (2) fractional calculus, design corresponding fractional order dynamic stability. The drive system of the fractional order cell neural network in difference construction step (3) and responding system.
Step (5): design isochronous controller and parameter adaptive regulation, realizes driving the synchronization with responding system in numerical simulation.
Step (6): fractional order cell neural network drive system in design procedure (4) and responding system circuit theory diagrams, controller and self-adaptative adjustment rate to step (5) realize circuit simulation simultaneously.
Further, a kind of fractional order cell neural network Self-adaptive synchronization control method of the present invention, it specifically comprises the following steps that
(S1): according to cytocidal action lattice basic model, integer rank three-dimensional cell nerve network system, the parameters a in adjustment state equation are first designedj,ajk,Sjk,(j=1,2,3, k=1,2,3), make system output chaos phenomenon;
And apply MATLAB software designed system is carried out numerical simulation, and observe its chaotic characteristic and attractor phasor;
(S2): definition and algorithm for fractional order differential have the definition of Cauchy integral formula, Grunwald-Letnikov fractional order integration, the definition of Riemann-Liouville fractional order differential, Caputo definition etc., the present invention selects to adopt the fractional calculus of Caputo definition, and its mathematic(al) representation is as follows:
�� () in formula is Gamma function, and n-1��q��n, q is mark, and n is integer;
Fractional Differential Equation corresponding to dynamic system can be expressed as:
Wherein vn,vn-1��v0And ��m,��m-1����0Represent corresponding fractional order rank value, a respectivelyn,��,a0And bm,��,b0For real number; In formula, (x, y) inputs F for system, and (x, y) exports G for system;
(S3): build fractional order synchronous control system model:
Wherein X �� RnIt is a n dimension state vector of drive system, h:Rn��Rn, h is split as linear processes two parts, then drive system I is:
In formula: X �� R is the state variable of drive system, g:Rn��RnFor comprising the continuous vector function of linear term, G (x) ATFor non-linear partial, G:Rn��Rn��nFor parameter vector function, A is the parameter matrix of the nonlinear function of drive system;
Corresponding responding system II is:
Y �� R in formula is in response to the state variable of system, U �� RnFor controller,It it is the parameter matrix of the nonlinear function of drive system;
(S4): the integer rank three-dimensional cell neutral net built based on step (S1), corresponding fractional order dynamic stability is gone out in combination with step (S2) fractional calculus Design Theory, formula (5) drive system I definition in integrating step (S3), constructs the drive system equation of this three-dimensional fractional order cell neural network:
Nonlinear parameter a in formula11,a12,a22It is given value, formula (6) the responding system II definition in integrating step (S3), the responding system equation of the three-dimensional fractional order cell neural network of structure:
Nonlinear parameter in formulaIt is unknown-value.
(S5): the isochronous controller U of (6) formula and parameter adaptive regulation in design procedure (S3), utilize mathematical theory to carry out proving to synchronize character, and undertaken emulate by MATLAB program and synchronize verify;
Drive and the error of response be:
Isochronous controller U:
U=[u1,u2,u3](10)
Wherein:
Selecting system self-adaptative adjustment rule is simultaneously:
Wherein ei(i=1,2,3) for the error of drive system Yu responding system;
(S6): design fractional order dynamic stability drive system (7) and responding system (8) circuit theory diagrams, and realize circuit simulation by Multisim design con-trol device (10) and self-adaptative adjustment rate (12).
The circuit design method of fractional order cell neural network Self-adaptive synchronization control method of the present invention, is characterized in that comprising the following steps:
(SS1) its corresponding integer rank circuit is designed according to integer rank three-dimensional cell nerve network system formula (1) built in claim 1 step (S1);
(SS2) design relates to the nonlinear object function in claim 1 step (S1) cell neural network in the three-dimensional cell nerve network system circuit design of step (SS1) integer rankModule;
(SS3) the fractional order value (q1=q2=q3=0.95) that selection is determined, and design the fractional order element circuit of this fractional order value correspondence rank value, including chain, tree-shaped, mixed type or novel;
(SS4) select the electric capacity in the circuit of designed integer rank in suitable fractional order element circuit replacement step (SS1), obtain the corresponding fractional order driving system circuit of system;
(SS5) formula (10) formula controller U and formula (12) formula self-adaptative adjustment rate being updated to the responding system formula (8) in claim 1 step (S4), the system of meeting with a response is:
Design nonlinear factorWithIntegrating circuit, design responding system circuit further in accordance with responding system equation (13);
(SS6) to drive circuit in step (SS4) and in step (SS5) response circuit carry out circuit integrated emulation, the synchronization character of checking design system.
Present invention is characterized in that this system is fractional order dynamic stability compared with traditional cell neural network, in designed drive response synchro system, the nonlinear parameter of drive system is it is known that and the nonlinear parameter of responding system is unknown. But still make this drive response system realize Synchronization Control by designing isochronous controller and parameter adaptive regulation. In conjunction with fractional order circuit, theoretical and multiplexed combination circuit thought, have devised corresponding synchronization control circuit schematic diagram. Simulation result shows that circuit simulation has similar synchronization phasor with numerical simulation, demonstrate this Systems Theory analyze correctness and actual physics on realizability.
Accompanying drawing explanation
The chaos attractor phasor that Fig. 1 fractional order dynamic stability numerical computations produces. A () is variable x1-x2, (b) is variable x2-x3, (c) is variable x1-x3��
Fig. 2 fractional order CNN adaptive synchronicity system model variable and error curve diagram. Wherein (a) is for driving and response variable xi-yi(i=1,2,3) variation track curve chart, (b) is system model error ei(i=1,2,3) Asymptotic Synchronization figure.
Fig. 3 fractional order CNN drive system (driver) circuit theory diagrams. Wherein (a) fractional order CNN drive system (driver) circuit theory diagrams, (b) is drive system (driver) equivalent circuit diagram.
Fig. 4 fractional order CNN driving system circuit simulation result phasor. A () is variable x1-x2, (b) is variable x2-x3, (c) is variable x1-x3��
Fig. 5 fractional order CNN responding system circuit theory diagrams.
Fig. 6 fractional order CNN drive response system xi-yi(i=1,2,3) Simulation results. A () is variable x1-y1, (b) is variable x2-y2, (c) is variable x3-y3��
Fig. 7 f (x) module FX circuit theory diagrams and simulation waveform thereof. A () is circuit theory diagrams, (b) is circuit simulation waveform, and (c) is equivalent circuit diagram.
Fig. 8 fractional order each unit circuit diagram. Wherein, (a) is chain element circuit; (b) tree-shaped element circuit; C () is mixed type element circuit; D () is Novel unit circuit.
Detailed description of the invention
Below with reference to accompanying drawing, the present invention is described in further detail.
Embodiment:
1, adopting the fractional calculus of Caputo definition, its mathematic(al) representation is as follows:
�� () in formula is Gamma function, and n-1��q��n, q is mark, and n is integer, and the Laplace of this formula converts expression formula and is:
If the initial condition of function f (t) is zero, then formula (14) can be simplified shown as:
Fractional Differential Equation for its correspondence of dynamic system can be expressed as:
Wherein vn,vn-1��v0And ��m,��m-1����0Represent corresponding fractional order rank value respectively. In formula, (x, y) inputs F for system, and (x y) exports, it is assumed that they are satisfied by the condition that initial value is 0 G for system. It is done Laplace conversion, it is possible to the transmission function obtaining Fractional Differential Equation is:
It is not difficult to find out from formula (17): transfer function H (s)=1/s can be used in a frequency domainqRepresent fractional order differential operator q.
2, in order to new fractional order cell neural network can produce stable chaos phenomenon, the matrix parameter of system (7) is made to be chosen as:
Fractional order drive system (7) equation is changed to:
(18) three Lyapunov index respectively L in formula1=5.0529, L2=-1.2626, L3=-1.7904, its maximum is more than zero. And the Lyapunov dimension of system is:
Therefore this system creates chaos phenomenon, and designed system is carried out numerical simulation and observes its chaotic characteristic with attractor phasor as it is shown in figure 1, also indicate that and which create chaos phenomenon by MATLAB simultaneously.
3, according to (6) formulaCorresponding fractional order responding system is:
(19) nonlinear parameter in formulaIt is unknown-value.
3, design isochronous controller and parameter adaptive regulation.
Isochronous controller U is deployable is:
Wherein ei=yi-xi,
Building a Lyapunov-krasovskii functional function is:
Selecting system self-adaptative adjustment rule is simultaneously:
Conclusion can be obtained: work as s by theoretical derivation11�� 1, s22�� 1, s33When��1, V'(t in formula (20))��0, namely have:Set up, and obviously have V (t) >=0, therefore error
Therefore responding system Y and drive system X tends to Tong Bu, namely has during t �� ��, Y-X �� 0,
With MATLAB Numerical Simulation Results as shown in Figure 2.
4, linear resistance, linear capacitance, operational amplifier LM741 and fractional order element circuit are utilized, design fractional order cell neural network driving system circuit schematic diagram is as shown in Figure 3, and carrying out circuit simulation, simulation result is similar to Numerical Simulation Results Fig. 1, and simulation result is as shown in Figure 4.
5, the equation according to self-adaptative adjustment rate designs nonlinear factorWithIntegrating circuit figure, responding system circuit can be designed further in accordance with responding system equation; Can designing circuit theory Fig. 5 institute of overall Self-adaptive synchronization control system in conjunction with drive system Fig. 3, and utilize Multisim to be driven-respond synchronization simulation, simulation result is as shown in Figure 6
6, drive and response circuit relates to the nonlinear object function in cell neural network (1)Module, it uses amplifier TL082CD design when �� 18V to realize; The circuit diagram of design is as shown in Figure 7.
7, reality of the present invention can realize 4096 kinds of multiplexed combination fractional order circuits, for brevity, chooses fractional order qi(i=1,2,3) identical value (i.e. q1=q2=q3=0.95) chain, tree-shaped, mixed type, novel four kinds of combinations. Its complex frequency domain expression formula is respectively as follows:
(a) chain
(b) tree-shaped
(c) mixed type
D () is novel
The component parameters of each unit circuit is as shown in table 1, and corresponding circuit diagram is as shown in Figure 8.
Table 1 fractional order each unit circuit element parameter
Claims (2)
1. a fractional order cell neural network Self-adaptive synchronization control method, is characterized in that comprising the following steps:
(S1) according to cytocidal action lattice basic model, first design integer rank three-dimensional cell nerve network system, the parameters in adjustment state equationMake system output chaos phenomenon;
And apply MATLAB software designed system is carried out numerical simulation;
(S2) fractional order differential algorithm is selected: selecting the fractional calculus of Caputo definition, its mathematic(al) representation is as follows:
�� () in formula is Gamma function, and n-1��q��n, q is mark, and n is integer;
Fractional Differential Equation corresponding to dynamic system can be expressed as:
Wherein vn,vn-1��v0And ��m,��m-1����0Represent corresponding fractional order rank value, a respectivelyn,��,a0And bm,��,b0For real number; In formula, (x, y) inputs F for system, and (x, y) exports G for system;
(S3) fractional order synchronous control system model is built:
Wherein X �� RnIt is a n dimension state vector of drive system, h:Rn��Rn, h is split as linear processes two parts, then drive system I is:
In formula: X �� R is the state variable of drive system, g:Rn��RnFor comprising the continuous vector function of linear term, G (x) ATFor non-linear partial, G:Rn��Rn��nFor parameter vector function, A is the parameter matrix of the nonlinear function of drive system;
Corresponding responding system II is:
Y �� R in formula is in response to the state variable of system, U �� RnFor controller,It it is the parameter matrix of the nonlinear function of drive system;
(S4) the integer rank three-dimensional cell nerve network system built based on step (S1), designs corresponding fractional order dynamic stability in combination with step (S2) fractional calculus equation; Define in conjunction with formula (5) the drive system I in (S3), construct the drive system equation of this three-dimensional fractional order cell neural network:
Nonlinear parameter a in formula11,a12,a22It is given value; Define in conjunction with formula (6) the responding system II in (S3), the responding system equation of the three-dimensional fractional order cell neural network of structure:
Nonlinear parameter in formulaIt is unknown-value;
(S5) the isochronous controller U of (5) formula and parameter adaptive regulation in design procedure (S3), utilizes mathematical theory to carry out proving to synchronize character, and is undertaken emulate by MATLAB program and synchronize verify;
The error of drive system and responding system is:
Isochronous controller U:
U=[u1,u2,u3](10)
Wherein:
Selecting system self-adaptative adjustment rule is simultaneously:
Wherein ei(i=1,2,3) for the error of drive system Yu responding system;
(S6) design fractional order dynamic stability drive system formula (7) and responding system formula (8) circuit theory diagrams, and realize circuit simulation with Multisim design con-trol device formula (10) and self-adaptative adjustment rate formula (12).
2. the circuit design method of the fractional order cell neural network Self-adaptive synchronization control method described in claims 1, is characterized in that comprising the following steps:
(SS1) its corresponding integer rank circuit is designed according to integer rank three-dimensional cell nerve network system formula (1) built in claim 1 step (S1);
(SS2) design relates to the nonlinear object function in claim 1 step (S1) cell neural network in the three-dimensional cell nerve network system circuit design of step (SS1) integer rankModule;
(SS3) the fractional order value (q1=q2=q3=0.95) that selection is determined, and design the fractional order element circuit of this fractional order value correspondence rank value, including chain, tree-shaped, mixed type or novel;
(SS4) select the electric capacity in the circuit of designed integer rank in suitable fractional order element circuit replacement step (SS1), obtain the corresponding fractional order driving system circuit of system;
(SS5) formula (10) formula controller U and formula (12) formula self-adaptative adjustment rate being updated to the responding system formula (8) in claim 1 step (S4), the system of meeting with a response is:
Design nonlinear factorWithIntegrating circuit, design responding system circuit further in accordance with responding system equation (13);
(SS6) to drive circuit in step (SS4) and in step (SS5) response circuit carry out circuit integrated emulation.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201610065857.0A CN105629733B (en) | 2016-02-01 | 2016-02-01 | A kind of fractional order cell neural network Self-adaptive synchronization control and circuit design method |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201610065857.0A CN105629733B (en) | 2016-02-01 | 2016-02-01 | A kind of fractional order cell neural network Self-adaptive synchronization control and circuit design method |
Publications (2)
Publication Number | Publication Date |
---|---|
CN105629733A true CN105629733A (en) | 2016-06-01 |
CN105629733B CN105629733B (en) | 2018-05-01 |
Family
ID=56044802
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN201610065857.0A Active CN105629733B (en) | 2016-02-01 | 2016-02-01 | A kind of fractional order cell neural network Self-adaptive synchronization control and circuit design method |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN105629733B (en) |
Cited By (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN106160996A (en) * | 2016-07-04 | 2016-11-23 | 江西理工大学 | The circuit design method of any fractional order value based on general Lucas number |
CN108762067A (en) * | 2018-04-28 | 2018-11-06 | 南京理工大学 | A kind of the networking Synchronizing Control Devices and acquisition methods of memristor neural network |
CN109086874A (en) * | 2018-08-07 | 2018-12-25 | 穆天机器人(杭州)有限公司 | A kind of general neural network model based on Fractal structural theory |
CN110324137A (en) * | 2019-02-27 | 2019-10-11 | 齐鲁工业大学 | A kind of hiding chaos system of the fractional order with line balancing point |
CN110488634A (en) * | 2019-09-03 | 2019-11-22 | 江西理工大学 | Reverse sync is realized in coupled oscillator system and rotates the method for reverse sync |
CN113095497A (en) * | 2021-05-06 | 2021-07-09 | 安徽大学 | Finite time synchronization method and device for fractional order quaternary memristor neural network |
Citations (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP1220063B1 (en) * | 2000-12-27 | 2005-03-09 | STMicroelectronics S.r.l. | Non-integer order dynamic systems |
CN102385659A (en) * | 2011-12-13 | 2012-03-21 | 滨州学院 | Method for realizing fractional-order three-system automatic-switchover chaotic system and analog circuit |
CN103634097A (en) * | 2013-12-03 | 2014-03-12 | 西北农林科技大学 | Simplest element circuit with synchronous integral orders and fractional orders |
CN103970017A (en) * | 2013-12-02 | 2014-08-06 | 西北农林科技大学 | TS fuzzy control based synchronizing method for fractional order chaotic system and integer order chaotic system |
CN104298110A (en) * | 2014-09-26 | 2015-01-21 | 江西理工大学 | Method for designing delayed stable control circuit of different-fractional-order time-lag chaotic system |
CN104573817A (en) * | 2015-01-20 | 2015-04-29 | 江西理工大学 | Fractional order switchable multi-element circuit design method for variable parameter cell neural network |
-
2016
- 2016-02-01 CN CN201610065857.0A patent/CN105629733B/en active Active
Patent Citations (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
EP1220063B1 (en) * | 2000-12-27 | 2005-03-09 | STMicroelectronics S.r.l. | Non-integer order dynamic systems |
CN102385659A (en) * | 2011-12-13 | 2012-03-21 | 滨州学院 | Method for realizing fractional-order three-system automatic-switchover chaotic system and analog circuit |
CN103970017A (en) * | 2013-12-02 | 2014-08-06 | 西北农林科技大学 | TS fuzzy control based synchronizing method for fractional order chaotic system and integer order chaotic system |
CN103634097A (en) * | 2013-12-03 | 2014-03-12 | 西北农林科技大学 | Simplest element circuit with synchronous integral orders and fractional orders |
CN104298110A (en) * | 2014-09-26 | 2015-01-21 | 江西理工大学 | Method for designing delayed stable control circuit of different-fractional-order time-lag chaotic system |
CN104573817A (en) * | 2015-01-20 | 2015-04-29 | 江西理工大学 | Fractional order switchable multi-element circuit design method for variable parameter cell neural network |
Cited By (7)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN106160996A (en) * | 2016-07-04 | 2016-11-23 | 江西理工大学 | The circuit design method of any fractional order value based on general Lucas number |
CN108762067A (en) * | 2018-04-28 | 2018-11-06 | 南京理工大学 | A kind of the networking Synchronizing Control Devices and acquisition methods of memristor neural network |
CN109086874A (en) * | 2018-08-07 | 2018-12-25 | 穆天机器人(杭州)有限公司 | A kind of general neural network model based on Fractal structural theory |
CN110324137A (en) * | 2019-02-27 | 2019-10-11 | 齐鲁工业大学 | A kind of hiding chaos system of the fractional order with line balancing point |
CN110488634A (en) * | 2019-09-03 | 2019-11-22 | 江西理工大学 | Reverse sync is realized in coupled oscillator system and rotates the method for reverse sync |
CN110488634B (en) * | 2019-09-03 | 2022-06-10 | 江西理工大学 | Method for realizing reverse synchronization and rotation reverse synchronization in coupled oscillator system |
CN113095497A (en) * | 2021-05-06 | 2021-07-09 | 安徽大学 | Finite time synchronization method and device for fractional order quaternary memristor neural network |
Also Published As
Publication number | Publication date |
---|---|
CN105629733B (en) | 2018-05-01 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN105629733A (en) | Fractional order cell neural network adaptive synchronization control and circuit design method | |
Pham et al. | A simple three-dimensional fractional-order chaotic system without equilibrium: Dynamics, circuitry implementation, chaos control and synchronization | |
CN103646152B (en) | Electromagnetic transient simulation method for power system based on matrix index | |
Vaidyanathan | Analysis, control, and synchronization of a 3-D novel jerk chaotic system with two quadratic nonlinearities | |
Kingni et al. | A chaotic system with an infinite number of equilibrium points located on a line and on a hyperbola and its fractional-order form | |
CN105978725B (en) | Non-fragile distributed fault estimation method based on sensor network | |
Khan et al. | Analysis and hyper-chaos control of a new 4-D hyper-chaotic system by using optimal and adaptive control design | |
CN104298809A (en) | Nonlinear modeling solving method based on matrix index electromagnetic transient simulation | |
Zheng | Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling | |
CN105629721A (en) | Second-order nonlinear system no-model control method based on instruction filtering Backstepping | |
CN104156542A (en) | Implicit-projection-based method for simulating stability of active power distribution system | |
CN103077268A (en) | State space automatic modeling method orienting electromagnetic transient simulation of power system | |
CN104573817B (en) | A kind of changeable multiple circuit design method of the fractional order of variable element cell neural network | |
CN104298110B (en) | Method for designing delayed stable control circuit of different-fractional-order time-lag chaotic system | |
CN104202155A (en) | Synchronous time delay control circuit design method of different fractional order time lag chaotic system | |
Lai et al. | Heterogeneous coexisting attractors, large-scale amplitude control and finite-time synchronization of central cyclic memristive neural networks | |
CN106160997B (en) | A kind of New Grid sine chamber hyperchaotic map system | |
CN105573120A (en) | Multi-agent-based non-linear multi-simple-pendulum network system coordination control method | |
Xiang et al. | Analysis of pinning-controlled networks: A renormalization approach | |
CN109858191B (en) | Generalized chaotic synchronization system construction and circuit design method | |
Zhang et al. | Compound synchronization based on memristive cellular neural network of chaos system | |
CN103162846B (en) | Method for constructing coefficient conversion matrix between Zernike polynomial aberration mode and Walsh function aberration mode | |
CN104749957A (en) | Method for accurately configuring all Lyapunov indexes of constant discrete linear system | |
Zhu et al. | Modeling and adaptive pinning synchronization control for a chaotic-motion motor in complex network | |
CN106126871A (en) | A kind of governor model modeling method of PSCAD electromagnetic transient simulation |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
C06 | Publication | ||
PB01 | Publication | ||
C10 | Entry into substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
GR01 | Patent grant | ||
GR01 | Patent grant |