The Dynamics of a Predator-Prey System with State-Dependent Feedback Control | Zendy

Hunki Baek | Zendy

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The Dynamics of a Predator-Prey System with State-Dependent Feedback Control

Author(s) -

Hunki Baek

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/101386

Subject(s) - mathematics , bifurcation , period doubling bifurcation , control theory (sociology) , bifurcation diagram , chaotic , cascade , type (biology) , mathematical analysis , nonlinear system , control (management) , physics , computer science , chemistry , chromatography , quantum mechanics , artificial intelligence , biology , ecology

A Lotka-Volterra-type predator-prey system with state-dependent feedback control is investigated in both theoretical and numerical ways. Using the Poincaré map and the analogue of the Poincaré criterion, the sufficient conditions for the existence and stability of semitrivial periodic solutions and positive periodic solutions are obtained. In addition, we show that there is no positive periodic solution with period greater than and equal to three under some conditions. The qualitative analysis shows that the positive period-one solution bifurcates from the semitrivial solution through a fold bifurcation. Numerical simulations to substantiate our theoretical results are provided. Also, the bifurcation diagrams of solutions are illustrated by using the Poincaré map, and it is shown that the chaotic solutions take place via a cascade of period-doubling bifurcations

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