Volume 4, Issue 2
Spatial Dynamics of a Diffusive Prey-Predator Model with Stage Structure and Fear Effect

Nana Zhu & Sanling Yuan

J. Nonl. Mod. Anal., 4 (2022), pp. 392-408.

Published online: 2022-06

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

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  • Abstract

To understand the influence of fear effect on population dynamics, especially for the populations with obvious stage structure characteristics, we propose and investigate a diffusive prey-predator model with stage structure in predators. First, we discuss the existence and stability of equilibrium of the model in the absence of diffusion. Then, we obtain the critical conditions for Hopf and Turing bifurcations. Some numerical simulations are also carried out to verify our theoretical results, which indicate that the fear can induce the prey population to show five pattern structures: cold-spot pattern, mixed pattern with cold spots and stripes, stripes pattern, hot-spot pattern, mixed pattern with hot spots and stripes. These findings imply that the fear effect induced by the mature predators plays an important role in the spatial distribution of species.

  • AMS Subject Headings

92C10, 92C15

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COPYRIGHT: © Global Science Press

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@Article{JNMA-4-392, author = {Zhu , Nana and Yuan , Sanling}, title = {Spatial Dynamics of a Diffusive Prey-Predator Model with Stage Structure and Fear Effect}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {2}, pages = {392--408}, abstract = {

To understand the influence of fear effect on population dynamics, especially for the populations with obvious stage structure characteristics, we propose and investigate a diffusive prey-predator model with stage structure in predators. First, we discuss the existence and stability of equilibrium of the model in the absence of diffusion. Then, we obtain the critical conditions for Hopf and Turing bifurcations. Some numerical simulations are also carried out to verify our theoretical results, which indicate that the fear can induce the prey population to show five pattern structures: cold-spot pattern, mixed pattern with cold spots and stripes, stripes pattern, hot-spot pattern, mixed pattern with hot spots and stripes. These findings imply that the fear effect induced by the mature predators plays an important role in the spatial distribution of species.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.392}, url = {http://global-sci.org/intro/article_detail/jnma/20714.html} }
TY - JOUR T1 - Spatial Dynamics of a Diffusive Prey-Predator Model with Stage Structure and Fear Effect AU - Zhu , Nana AU - Yuan , Sanling JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 392 EP - 408 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.392 UR - https://global-sci.org/intro/article_detail/jnma/20714.html KW - Prey-predator model, Fear effect, Stage-structured model, Hopf bifurcation, Turing bifurcation, Pattern formation. AB -

To understand the influence of fear effect on population dynamics, especially for the populations with obvious stage structure characteristics, we propose and investigate a diffusive prey-predator model with stage structure in predators. First, we discuss the existence and stability of equilibrium of the model in the absence of diffusion. Then, we obtain the critical conditions for Hopf and Turing bifurcations. Some numerical simulations are also carried out to verify our theoretical results, which indicate that the fear can induce the prey population to show five pattern structures: cold-spot pattern, mixed pattern with cold spots and stripes, stripes pattern, hot-spot pattern, mixed pattern with hot spots and stripes. These findings imply that the fear effect induced by the mature predators plays an important role in the spatial distribution of species.

Zhu , Nana and Yuan , Sanling. (2022). Spatial Dynamics of a Diffusive Prey-Predator Model with Stage Structure and Fear Effect. Journal of Nonlinear Modeling and Analysis. 4 (2). 392-408. doi:10.12150/jnma.2022.392
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