Abstract
This paper deals with the stability, bifurcations and chaotic behaviors of discrete dynamical systems by using methods of symbolic computation. We explain how to reduce the problems of analyzing the stability, bifurcations and chaos induced by snapback repellers to algebraic problems, and solve them by using an algorithmic approach based on methods for solving semi-algebraic systems. The feasibility of the symbolic approach is demonstrated by analyses of the dynamical behaviors for several discrete models.
This work was done while Bo Huang was visiting NYU Courant. The first author wishes to thank Professor Chee Yap for his profound concern. Both authors thank Professor Dongming Wang for his valuable suggestions and the anonymous referees for their helpful comments on improving the presentation. The work was partially supported by China Scholarship Council (No. 201806020128), by the Academic Excellent Foundation of BUAA for PhD Students, by the NSF grant #CCF-1708884, and by the NSFC project 11601023.
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Huang, B., Niu, W. (2020). Algebraic Analysis of Bifurcations and Chaos for Discrete Dynamical Systems. In: Slamanig, D., Tsigaridas, E., Zafeirakopoulos, Z. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2019. Lecture Notes in Computer Science(), vol 11989. Springer, Cham. https://doi.org/10.1007/978-3-030-43120-4_14
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