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Volume 1, Issue 1
Nonexistence of Nonconstant Positive Steady States of a Diffusive Predator-Prey Model with Fear Effect

Shanshan Chen, Zonghao Liu & Junping Shi

DOI: 10.12150/jnma.2019.47

J. Nonl. Mod. Anal., 1 (2019), pp. 47-56.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

Reaction-diffusion, fear effect, global stability, nonexistence of nonconstant steady states.

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COPYRIGHT: © Global Science Press

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@Article{JNMA-1-47, author = {Chen , ShanshanLiu , Zonghao and Shi , Junping}, title = {Nonexistence of Nonconstant Positive Steady States of a Diffusive Predator-Prey Model with Fear Effect}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {1}, number = {1}, pages = {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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2019.47}, url = {http://global-sci.org/intro/article_detail/jnma/18867.html} }
TY - JOUR T1 - Nonexistence of Nonconstant Positive Steady States of a Diffusive Predator-Prey Model with Fear Effect AU - Chen , Shanshan AU - Liu , Zonghao AU - Shi , Junping JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 47 EP - 56 PY - 2021 DA - 2021/04 SN - 1 DO - http://doi.org/10.12150/jnma.2019.47 UR - https://global-sci.org/intro/article_detail/jnma/18867.html KW - Reaction-diffusion, fear effect, global stability, nonexistence of nonconstant steady states. AB -

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.

Shanshan Chen, Zonghao Liu & Junping Shi. (1970). Nonexistence of Nonconstant Positive Steady States of a Diffusive Predator-Prey Model with Fear Effect. Journal of Nonlinear Modeling and Analysis. 1 (1). 47-56. doi:10.12150/jnma.2019.47
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