Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model

Bifurcation theory (center manifold and Ljapunov-Schmidt reduction, normal form theory, universal unfolding, calculation of bifurcation diagrams) has become an important and very useful means in the solution of nonlinear stability problems in many branches of engineering. The present study deals wit...

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Bibliographic Details
Published in:IEEE access 2020, Vol.8, p.126760-126775
Main Authors: Lin, Youping, Din, Qamar, Rafaqat, Muhammad, Elsadany, Abdelalim A., Zeng, Yanqiu
Format: Article
Language:English
Subjects:
Asymptotic properties
Bifurcation
Bifurcation theory
Biological system modeling
Canonical forms
Chaos
chaos control
Chaos theory
Control methods
Discrete time systems
Existence theorems
Feedback control
flip bifurcation
Hopf bifurcation
Hybrid control
Lotka-Volterra model
Mathematical model
Mathematical models
Numerical models
Predator prey systems
Predator-prey simulation
stability
Stability analysis
Two dimensional models
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Summary:Bifurcation theory (center manifold and Ljapunov-Schmidt reduction, normal form theory, universal unfolding, calculation of bifurcation diagrams) has become an important and very useful means in the solution of nonlinear stability problems in many branches of engineering. The present study deals with qualitative behavior of a two-dimensional discrete-time system for interaction between prey and predator. The discrete-time model has more chaotic and rich dynamical behavior as compare to its continuous counterpart. We investigate the qualitative behavior of a discrete-time Lotka-Volterra model with linear functional response for prey. The local asymptotic behavior of equilibria is discussed for discrete-time Lotka-Volterra model. Furthermore, with the help of bifurcation theory and center manifold theorem, explicit parametric conditions for directions and existence of flip and Hopf bifurcations are investigated. Moreover, two chaos control methods, that is, OGY feedback control and hybrid control strategy, are implemented. Numerical simulations are provided to illustrate theoretical discussion and their effectiveness.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2020.3008522