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Complex Dynamics on the Routes to Chaos in a Discrete Predator-Prey System with Crowley-Martin Type Functional Response
Joint Authors
Huang, Tousheng
Zhang, Huayong
Cong, Xuebing
Zhang, Fei-Fan
Gao, Zichun
Ma, Shengnan
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-04-29
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
We present in this paper an investigation on a discrete predator-prey system with Crowley-Martin type functional response to know its complex dynamics on the routes to chaos which are induced by bifurcations.
Via application of the center manifold theorem and bifurcation theorems, occurrence conditions for flip bifurcation and Neimark-Sacker bifurcation are determined, respectively.
Numerical simulations are performed, on the one hand, verifying the theoretical results and, on the other hand, revealing new interesting dynamical behaviors of the discrete predator-prey system, including period-doubling cascades, period-2, period-3, period-4, period-5, period-6, period-7, period-8, period-9, period-11, period-13, period-15, period-16, period-20, period-22, period-24, period-30, and period-34 orbits, invariant cycles, chaotic attractors, sub-flip bifurcation, sub-(inverse) Neimark-Sacker bifurcation, chaotic interior crisis, chaotic band, sudden disappearance of chaotic dynamics and abrupt emergence of chaos, and intermittent periodic behaviors.
Moreover, three-dimensional bifurcation diagrams are utilized to study the transition between flip bifurcation and Neimark-Sacker bifurcation, and a critical case between the two bifurcations is found.
This critical bifurcation case is a combination of flip bifurcation and Neimark-Sacker bifurcation, showing the nonlinear characteristics of both bifurcations.
American Psychological Association (APA)
Zhang, Huayong& Ma, Shengnan& Huang, Tousheng& Cong, Xuebing& Gao, Zichun& Zhang, Fei-Fan. 2018. Complex Dynamics on the Routes to Chaos in a Discrete Predator-Prey System with Crowley-Martin Type Functional Response. Discrete Dynamics in Nature and Society،Vol. 2018, no. 2018, pp.1-18.
https://search.emarefa.net/detail/BIM-1152371
Modern Language Association (MLA)
Zhang, Huayong…[et al.]. Complex Dynamics on the Routes to Chaos in a Discrete Predator-Prey System with Crowley-Martin Type Functional Response. Discrete Dynamics in Nature and Society No. 2018 (2018), pp.1-18.
https://search.emarefa.net/detail/BIM-1152371
American Medical Association (AMA)
Zhang, Huayong& Ma, Shengnan& Huang, Tousheng& Cong, Xuebing& Gao, Zichun& Zhang, Fei-Fan. Complex Dynamics on the Routes to Chaos in a Discrete Predator-Prey System with Crowley-Martin Type Functional Response. Discrete Dynamics in Nature and Society. 2018. Vol. 2018, no. 2018, pp.1-18.
https://search.emarefa.net/detail/BIM-1152371
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1152371