Relaxation oscillation profile of limit cycle in  predator-prey system

Sze-Bi Hsu; Junping Shi

doi:10.3934/dcdsb.2009.11.893

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2009, Volume 11, Issue 4: 893-911. Doi: 10.3934/dcdsb.2009.11.893

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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: May 31, 2008

Revised: November 30, 2008

Published: October 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 34C26, Secondary: 34C15, 34C07, 92D25.

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