Stability, Neimark-Sacker bifurcation and chaos control for a prey-predator system with harvesting effect on predator

This paper deals with the dynamic behavior of a prey predator model obtained by the forward Euler method. We investigate the complex dynamics of discrete-time prey-predator system related to predator population which is subject to the effects of harvesting. The stability of equilibrium point of the...

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Published inMathematical notes (Miskolci Egyetem (Hungary)) Vol. 22; no. 2; pp. 663 - 679
Main Authors Gumus, Ozlem Ak, Feckan, Michal
Format Journal Article
LanguageEnglish
Published Miskolc University of Miskolc 2021
Subjects
Bifurcation theory
Control stability
Control theory
Discrete time systems
Eigenvalues
Equilibrium
Extinction
Mathematical models
Population
Predator-prey simulation
Predators
R&D
Research & development
Simulation
State feedback
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Summary:This paper deals with the dynamic behavior of a prey predator model obtained by the forward Euler method. We investigate the complex dynamics of discrete-time prey-predator system related to predator population which is subject to the effects of harvesting. The stability of equilibrium point of the model and also the existence and the direction of Neimark-Sacker bifurcation are analyzed. We show that the system undergoes Neimark-Sacker bifurcations by using center manifold theorem and bifurcation theory. A state feedback method is applied in order to control the Neimark-Sacker bifurcation. Moreover, numerical simulations are carried out to demonstrate the theoretical results obtained for stability, bifurcation and chaos control strategy.
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ISSN:1787-2405
1787-2413
DOI:10.18514/MMN.2021.3450