COMPLEXITY OF A DELAYED PREDATOR–PREY MODEL WITH IMPULSIVE HARVEST AND HOLLING TYPE II FUNCTIONAL RESPONSE

Guangzhao Zeng (), Fengyan Wang () and Juan J. Nieto ()
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Guangzhao Zeng: Department of Mathematics, Shaoguan University, Shaoguan, Guangdong, 512005, P. R. China
Fengyan Wang: College of Science, Jimei University, Xiamen, Fujian, 361021, P. R. China
Juan J. Nieto: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Spain

Advances in Complex Systems (ACS), 2008, vol. 11, issue 01, 77-97

Abstract: We study an impulsive delay differential predator–prey model with Holling type II functional response. The stability of the trivial equilibrium is analyzed by means of impulsive Floquet theory providing a sufficient condition for extinction. Using coincidence degree theory we show the existence of positive periodic solutions. The system is then analyzed numerically, revealing that the presence of delays and impulses may lead to chaotic solutions, quasi-periodic solutions, or multiple periodic solutions. Several simulations and examples are presented.

Keywords: Impulsive delayed differential equations; extinction; existence of periodic solution; coincidence degree; chaotic solution; quasi-periodic solution (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S0219525908001519

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