Bifurcation and chaos in a discrete Holling–Tanner model with Beddington–DeAngelis functional response

The dynamics of a discrete Holling–Tanner model with Beddington–DeAngelis functional response is studied. The permanence and local stability of fixed points for the model are derived. The center manifold theorem and bifurcation theory are used to show that the model can undergo flip and Hopf bifurca...

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Veröffentlicht in:Advances in continuous and discrete models Jg. 2023; H. 1; S. 41
Hauptverfasser: Yang, Run, Zhao, Jianglin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 23.10.2023
Springer Nature B.V
Schlagworte:
Analysis
Bifurcation theory
Centre manifold theory
Codes
Control methods
Difference and Functional Equations
Feedback control
Fixed points (mathematics)
Functional Analysis
Hopf bifurcation
Liapunov exponents
Mathematical models
Mathematics
Mathematics and Statistics
Orbital stability
Orbits
Ordinary Differential Equations
Partial Differential Equations
Predator-prey simulation
Chaos
1:2 resonance
Flip and Hopf bifurcation
Stability
Discrete predator–prey system
ISSN:2731-4235, 1687-1839, 2731-4235, 1687-1847
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Zusammenfassung:The dynamics of a discrete Holling–Tanner model with Beddington–DeAngelis functional response is studied. The permanence and local stability of fixed points for the model are derived. The center manifold theorem and bifurcation theory are used to show that the model can undergo flip and Hopf bifurcations. Codimension-two bifurcation associated with 1:2 resonance is analyzed by applying the bifurcation theory. Numerical simulations are performed not only to verify the correctness of theoretical analysis but to explore complex dynamical behaviors such as period-6, 7, 10, 12 orbits, a cascade of period-doubling, quasi-periodic orbits, and the chaotic sets. The maximum Lyapunov exponents validate the chaotic dynamical behaviors of the system. The feedback control method is considered to stabilize the chaotic orbits. These complex dynamical behaviors imply that the coexistence of predator and prey may produce very complex patterns.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2731-4235
1687-1839
2731-4235
1687-1847
DOI:10.1186/s13662-023-03788-y