Bifurcations, Complex Behaviors, and Dynamic Transition in a Coupled Network of Discrete Predator-Prey System
Joint Authors
Huang, Tousheng
Zhang, Huayong
Pan, Ge
Ma, Shengnan
Wang, Zhaodeng
Huang, Hai
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-06-13
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
The nonlinear dynamics of predator-prey systems coupled into network is an important issue in recent biological advances.
In this research, we consider each node of the coupled network represents a discrete predator-prey system, and the network dynamics is investigated.
By applying Jacobian matrix, center manifold theorem and bifurcation theorems, stability of fixed points, flip bifurcation and Neimark-Sacker bifurcation of the discrete predator-prey system are analyzed.
Via the method of Lyapunov exponents, the nonchaos-chaos transition of the coupled network along the routes to chaos induced by bifurcations is determined.
Numerical simulations are performed to demonstrate the bifurcations, various attractors and dynamic transitions of the coupled network.
Via comparison, we find that the coupled network exhibits far richer and more complex behaviors than single predator-prey system, including period-doubling cascades in orbits of period-2, period-4, period-8, invariant closed curves, dynamic windows for periodic orbits and invariant curves, quasiperiodic orbits, tori, and chaotic sets.
Moreover, the attractors of the coupled network show more diverse and complicated structures.
These results may provide a new perspective on the predator-prey dynamics in complex networks.
American Psychological Association (APA)
Huang, Tousheng& Zhang, Huayong& Ma, Shengnan& Pan, Ge& Wang, Zhaodeng& Huang, Hai. 2019. Bifurcations, Complex Behaviors, and Dynamic Transition in a Coupled Network of Discrete Predator-Prey System. Discrete Dynamics in Nature and Society،Vol. 2019, no. 2019, pp.1-22.
https://search.emarefa.net/detail/BIM-1146289
Modern Language Association (MLA)
Huang, Tousheng…[et al.]. Bifurcations, Complex Behaviors, and Dynamic Transition in a Coupled Network of Discrete Predator-Prey System. Discrete Dynamics in Nature and Society No. 2019 (2019), pp.1-22.
https://search.emarefa.net/detail/BIM-1146289
American Medical Association (AMA)
Huang, Tousheng& Zhang, Huayong& Ma, Shengnan& Pan, Ge& Wang, Zhaodeng& Huang, Hai. Bifurcations, Complex Behaviors, and Dynamic Transition in a Coupled Network of Discrete Predator-Prey System. Discrete Dynamics in Nature and Society. 2019. Vol. 2019, no. 2019, pp.1-22.
https://search.emarefa.net/detail/BIM-1146289
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1146289