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June  2009, 11(4): 893-911. doi: 10.3934/dcdsb.2009.11.893

Relaxation oscillation profile of limit cycle in predator-prey system

Sze-Bi Hsu 1, and  Junping Shi 2,

1. 

Department of Mathematics, National Tsing-Hua University, Hsin-Chu 30043
2. 

Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187

Received  June 2008 Revised  December 2008 Published  April 2009

It is known that some predator-prey system can possess a unique limit cycle which is globally asymptotically stable. For a prototypical predator-prey system, we show that the solution curve of the limit cycle exhibits temporal patterns of a relaxation oscillator, or a Heaviside function, when certain parameter is small.
Keywords: predator-prey model., limit cycle, Relaxation oscillator.
Mathematics Subject Classification: Primary: 34C26, Secondary: 34C15, 34C07, 92D2.
Citation: Sze-Bi Hsu, Junping Shi. Relaxation oscillation profile of limit cycle in predator-prey system. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 893-911. doi: 10.3934/dcdsb.2009.11.893
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