The dynamics of a delayed predator-prey model with state dependent feedback control

A delayed prey-predator model with state-dependent impulses is investigated. The sufficient conditions of existence and stability of semi-trivial solution and positive period-1 solution are obtained by using the Poincare map and analogue of the Poincare Criterion. The qualitative analysis shows that...

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Bibliographic Details
Main Authors: Singh, Anuraj, Gakkhar, Sunita
Format: Conference Proceeding
Language:English
Subjects:
BIFURCATION
CHAOS THEORY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COMPUTERIZED SIMULATION
CONTROL
DIFFERENTIAL EQUATIONS
EQUATIONS
FEEDBACK
MATHEMATICAL SOLUTIONS
MATHEMATICS
PREDATOR-PREY INTERACTIONS
SIMULATION
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Summary:A delayed prey-predator model with state-dependent impulses is investigated. The sufficient conditions of existence and stability of semi-trivial solution and positive period-1 solution are obtained by using the Poincare map and analogue of the Poincare Criterion. The qualitative analysis shows that the positive period-one solution bifurcates from the semi-trivial solution through a fold bifurcation. The complex dynamics including chaos is obtained and numerical simulations substantiate the analytical results.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.3663487