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Exact Solutions of a Diffusive Predator–Prey System by the Generalized Riccati Equation

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Abstract

We establish exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator–prey system where the prey per capita growth rate is subject to the Allee effect. Using the generalized Riccati equation, we derive exact solutions to this model for two different wave speed.

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Acknowledgments

The authors are grateful to the referee who suggests the main method and Dr. Norhashidah Ali who recommends our paper.

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, Suwon, 440-740, Republic of Korea

    Hyunsoo Kim

  2. Humanitas College, Kyung Hee University, Yongin, 446-701, Republic of Korea

    Jin Hyuk Choi

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  1. Hyunsoo Kim
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  2. Jin Hyuk Choi
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Correspondence to Jin Hyuk Choi.

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Communicated by Dr. Norhashidah M. Ali.

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Kim, H., Choi, J.H. Exact Solutions of a Diffusive Predator–Prey System by the Generalized Riccati Equation. Bull. Malays. Math. Sci. Soc. 39, 1125–1143 (2016). https://doi.org/10.1007/s40840-015-0219-9

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  • DOI: https://doi.org/10.1007/s40840-015-0219-9

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