SPATIOTEMPORAL DYNAMICS OF A PREDATOR-PREY MODEL INCORPORATING A PREY REFUGE

M. Sambath; K. Balachandran

doi:10.11948/2013006

2013 Volume 3 Issue 1

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M. Sambath, K. Balachandran. SPATIOTEMPORAL DYNAMICS OF A PREDATOR-PREY MODEL INCORPORATING A PREY REFUGE[J]. Journal of Applied Analysis & Computation, 2013, 3(1): 71-80. doi: 10.11948/2013006

Citation:

M. Sambath, K. Balachandran. SPATIOTEMPORAL DYNAMICS OF A PREDATOR-PREY MODEL INCORPORATING A PREY REFUGE[J]. Journal of Applied Analysis & Computation, 2013, 3(1): 71-80. doi: 10.11948/2013006

SPATIOTEMPORAL DYNAMICS OF A PREDATOR-PREY MODEL INCORPORATING A PREY REFUGE

Department of Mathematics, Bharathiar University, Coimbatore-641 046, India

Abstract

Abstract

In this paper, we investigate the spatiotemporal dynamics of a ratio-dependent predator-prey model with cross diffusion incorporating proportion of prey refuge. First we get the critical lines of Hopf and Turing bifurcations in a spatial domain by using mathematical theory. More specifically, the exact Turing region is given in a two parameter space. Also we perform a series of numerical simulations. The obtained results reveal that this system has rich dynamics, such as spotted, stripe and labyrinth patterns which show that it is useful to use the predator-prey model to reveal the spatial dynamics in the real world.
- Cross-diffusion /
- turing bifurcation /
- prey refuge /
- pattern formation
MSC: 92D25;70K50;35B36

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References

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