This paper is concerned with coexistence states of boundary value problems $$\begin{array}{c}\hfill \left\{\begin{array}{cc}\text{div}\left(d,(,v,),\mathrm{\nabla },u,-,u,\chi ,(,v,),\mathrm{\nabla },v\right)+\lambda u-u^2+\gamma uF(v)=0,\hfill & x\in \mathrm{\Omega },\hfill \\ D\mathrm{\Delta }v+\mu v-v^2-uF(v)=0,\hfill & x\in \mathrm{\Omega },\hfill \\ u=v=0,\hfill & x\in \partial \mathrm{\Omega }.\hfill \end{array}\right)\end{array}$$This is the stationary problem associated with the predator–prey system with prey-taxis, and u (resp. ...$$$$

Discrete time delay has been widely used in models of interacting populations to capture various biological processes such as gestation, maturation, food digestion, disease transmission and so on. In most of the works, it has been ...

• A dynamic green competition model based on bounded rationality is established.
• The stability analysis of equilibrium points and the complex dynamical behaviors are discussed in detail.
• The synchronization behaviors of two ...

Green and low carbon is an important way to coordinate economic and social development, which is also true for enterprises. Hence, the essay mainly builds up a green supply chain consisting of one supplier and two manufacturers. Gradient ...

A general reaction–diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady-state solutions are proved via studying an equivalent reaction–diffusion ...

In this paper, a general reaction–diffusive predator–prey system with prey-taxis subject to the homogeneous Neumann boundary condition is considered. Firstly, we investigate the local stability of the unique positive equilibrium by ...

In this paper, we study global bifurcation phenomena for the following Kirchhoff type problem { - M ( | u ( x ) | 2 d x ) Δ u = λ f ( x , u ) in , u = 0 on , where M is a continuous function. Under some natural hypotheses, we show that ( λ 1 ( a ) M ( 0 ...

In this paper, the Allee effect is incorporated into a predator-prey model with linear functional response. Compared with the predator-prey model without the Allee effect, it is found that the Allee effect of the prey species increases the extinction ...

In this paper, we shall establish unilateral global bifurcation result for a class of fourth-order eigenvalue problems with sign-changing weight. Under some natural hypotheses on perturbation function, we show that @m"k^@n,0 is a bifurcation point of ...

Using a combination of analytical and numerical methods, the global bifurcations and chaotic dynamics of two non-linearly coupled parametrically excited van der Pol oscillators are investigated in detail. With the aid of the method of multiple scales, ...

matcont is a matlab continuation package for the interactive numerical study of a range of parameterized nonlinear dynamical systems, in particular ODEs, that allows to compute curves of equilibria, limit points, Hopf points, limit cycles, flip, fold ...

We consider the nonlinear Sturm-Liouville boundary value problem {(Lu)(t)=@la(t)f(u(t)),0

In this paper, the number of limit cycles in a family of polynomial systems was studied by the bifurcation methods. With the help of a computer algebra system (e.g., Maple 7.0), we obtain that the least upper bound for the number of limit cycles ...