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Relaxation Oscillation Profile Of Limit Cycle In Predator-prey System.pdf

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Preview of Relaxation oscillation profile of limit cycle in predator-prey system
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📊 Size: 380 KB
📄 Pages: 19 pages
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Summary

The authors analyze a predator-prey system with a unique limit cycle that is globally asymptotically stable. They show that when the predator death rate is small, the solution curve of the limit cycle exhibits temporal patterns of a relaxation oscillator. The period of the limit cycle is of order O(λ−1), where λ is a parameter related to the predator death rate. The prey population is low for a time scale of O(λ−1), then spikes to reach the maximum in a time scale of O(| ln λ|), while the predator population reaches the maximum value from the minimum value in a time scale of O(| ln λ|), then slowly decays to the minimum value in a time scale of O(λ−1). The authors also consider the case where the parameter a tends to zero and find that the asymptotic profile of the limit cycle is different, with the predator population showing a spiky pulse shape and the prey population showing a profile of Heaviside function.

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The authors analyze a predator-prey system with a unique limit cycle that is globally asymptotically stable.

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  • File Format: PDF
  • File Size: 380 KB
  • Pages: 19
  • Language: EN
  • Total Downloads: 49
  • Last Updated: 3 weeks ago

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