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Communications on Pure and Applied Analysis (CPAA)
 

The effect of delay on a diffusive predator-prey system with Holling Type-II predator functional response

Pages: 481 - 501, Volume 12, Issue 1, January 2013      doi:10.3934/cpaa.2013.12.481

 
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Shanshan Chen - Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, China (email)
Junping Shi - Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187, United States (email)
Junjie Wei - Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, China (email)

Abstract: A delayed diffusive predator-prey system with Holling type-II predator functional response subject to Neumann boundary conditions is considered here. The stability/instability of nonnegative equilibria and associated Hopf bifurcation are investigated by analyzing the characteristic equations. By the theory of normal form and center manifold, an explicit formula for determining the stability and direction of periodic solution bifurcating from Hopf bifurcation is derived.

Keywords:  Predator-prey, delay, stability, Hopf bifurcation, periodic orbit.
Mathematics Subject Classification:  Primary: 35K57; Secondary: 35R10, 92D25.

Received: November 2010;      Revised: April 2012;      Available Online: September 2012.

 References