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January 2013, 12(1): 481-501. doi: 10.3934/cpaa.2013.12.481
The effect of delay on a diffusive predator-prey system with Holling Type-II predator functional response
Shanshan Chen 1, , Junping Shi 2, and Junjie Wei 1,
Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, China, China
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187
Received November 2010 Revised April 2012 Published September 2012
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: delay, Predator-prey, Hopf bifurcation, stability, periodic orbit..
Mathematics Subject Classification: Primary: 35K57; Secondary: 35R10, 92D2.
Citation: Shanshan Chen, Junping Shi, Junjie Wei. The effect of delay on a diffusive predator-prey system with Holling Type-II predator functional response. Communications on Pure & Applied Analysis, 2013, 12 (1) : 481-501. doi: 10.3934/cpaa.2013.12.481
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Shanshan Chen Junping Shi Junjie Wei