Bifurcation Analysis of a Time- and Space-Discrete Predator-Prey Model with Holling II Function Response

DOI

10.2991/mmsa-18.2018.10How to use a DOI?

Keywords

discrete model; coupled map lattice; hopf bifurcation; turing instability; pattern formation

Abstract

In this paper, a space- and time-discrete predator-prey model with Holling type II function response is investigated. The mortality of predator is variable, which is related to the population density. The model is given by a coupled map lattice framework, it takes a nonlinear relationship between predator-prey reaction stage and dispersal stage. The stability of equilibrium point and the parameter conditions for the Hopf bifurcation are obtained when the diffusion is absent. After adding the diffusion, we obtained the parameter conditions for the Turing instability. Numerical simulations verify the theoretical analysis and show a series of spatial patterns with the change of the parameters.

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  - Tianjiao Zhang
AU  - Yan Meng
AU  - Yongan Ye
PY  - 2018/03
DA  - 2018/03
TI  - Bifurcation Analysis of a Time- and Space-Discrete Predator-Prey Model with Holling II Function Response
BT  - Proceedings of the 2018 International Conference on Mathematics, Modelling, Simulation and Algorithms (MMSA 2018)
PB  - Atlantis Press
SP  - 39
EP  - 44
SN  - 1951-6851
UR  - https://doi.org/10.2991/mmsa-18.2018.10
DO  - 10.2991/mmsa-18.2018.10
ID  - Zhang2018/03
ER  -