Bifurcation Analysis of a Ratio-Dependent Holling-Tanner Model with Cross-Diffusion

DOI

10.2991/cimns-18.2018.36How to use a DOI?

Keywords

discrete model; hopf bifurcation; turing instability; pattern formation

Abstract

In this paper, we investigate a discrete space-time predator-prey model with ratio-dependent function response. The model is given by a coupled map lattice framework, it takes a nonlinear relationship between predator-prey reaction stage and dispersal stage. Through stability analysis and bifurcation analysis, the parameter conditions of Hopf bifurcation is obtained. When adding the cross-diffusion, we obtain the parameter conditions of Turing instability. Numerical simulations verify the theoretical analysis and show a series of spatial patterns.

Copyright

© 2018, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Zhen Li
AU  - Yan Meng
AU  - Yongan Ye
PY  - 2018/11
DA  - 2018/11
TI  - Bifurcation Analysis of a Ratio-Dependent Holling-Tanner Model with Cross-Diffusion
BT  - Proceedings of the 2018 3rd International Conference on Communications, Information Management and Network Security (CIMNS 2018)
PB  - Atlantis Press
SP  - 160
EP  - 165
SN  - 2352-538X
UR  - https://doi.org/10.2991/cimns-18.2018.36
DO  - 10.2991/cimns-18.2018.36
ID  - Li2018/11
ER  -