Nonexistence of Nonconstant Positive Steady States of a Diffusive Predator-Prey Model with Fear Effect
Year: 2019
Author: Shanshan Chen, Zonghao Liu, Junping Shi
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 1 : pp. 47–56
Abstract
In this paper, we investigate a diffusive predator-prey model with fear effect. It is shown that, for the linear predator functional response case, the positive constant steady state is globally asymptotically stable if it exists. On the other hand, for the Holling type II predator functional response case, it is proved that there exist no nonconstant positive steady states for large conversion rate. Our results limit the parameters range where complex spatiotemporal pattern formation can occur.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2019.47
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 1 : pp. 47–56
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Reaction-diffusion fear effect global stability nonexistence of nonconstant steady states.