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Relaxation oscillations in predator–prey model with distributed delay

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Abstract

The predator–prey model with distributed delay is stated in present paper. On the basis of geometric singular perturbation theory, the transition of the solution trajectory is illuminated, and the existence of the relaxation oscillation is proved. It is indicated the characteristic of the relaxation oscillation is dependent on the structure of the slow manifold. Moreover, the approximate expression of the relaxation oscillation and its period are obtained analytically. One case study is given to demonstrate the validity of theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Na Wang & Maoan Han

  2. Department of Applied Mathematics, Shanghai Institute of Technology, Shanghai, 201418, China

    Na Wang

Authors
  1. Na Wang
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  2. Maoan Han
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Correspondence to Na Wang.

Additional information

Communicated by Maria do Rosario de Pinho.

Project supported by the National Science Foundation of China (Grant No. 11401385).

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Wang, N., Han, M. Relaxation oscillations in predator–prey model with distributed delay. Comp. Appl. Math. 37, 475–484 (2018). https://doi.org/10.1007/s40314-016-0353-5

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  • DOI: https://doi.org/10.1007/s40314-016-0353-5

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