Cross-diffusion induced Turing patterns in a sex-structured predator-prey model

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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Cross-diffusion induced Turing patterns in a sex-structured predator-prey model. / Liu, J.; Zhou, H.; Zhang, Lai.

In: International Journal of Biomathematics, Vol. 5, No. 4, 2012.

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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Author

Liu, J.; Zhou, H.; Zhang, Lai / Cross-diffusion induced Turing patterns in a sex-structured predator-prey model.

In: International Journal of Biomathematics, Vol. 5, No. 4, 2012.

Publication: Research - peer-reviewJournal article – Annual report year: 2012

Bibtex

@article{722193a4e949404787daa6450f1044f0,
title = "Cross-diffusion induced Turing patterns in a sex-structured predator-prey model",
keywords = ", Predator-prey model, Cross-diffusion, Turing pattern, Sex structure",
publisher = "World Scientific Publishing Co. Pte. Ltd.",
author = "J. Liu and H. Zhou and Lai Zhang",
year = "2012",
doi = "10.1142/S179352451100157X",
volume = "5",
number = "4",
journal = "International Journal of Biomathematics",
issn = "1793-5245",

}

RIS

TY - JOUR

T1 - Cross-diffusion induced Turing patterns in a sex-structured predator-prey model

A1 - Liu,J.

A1 - Zhou,H.

A1 - Zhang,Lai

AU - Liu,J.

AU - Zhou,H.

AU - Zhang,Lai

PB - World Scientific Publishing Co. Pte. Ltd.

PY - 2012

Y1 - 2012

N2 - In this paper, we consider a sex-structured predator-prey model with strongly coupled nonlinear reaction diffusion. Using the Lyapunov functional and Leray-Schauder degree theory, the existence and stability of both homogenous and heterogenous steady-states are investigated. Our results demonstrate that the unique homogenous steady-state is locally asymptotically stable for the associated ODE system and PDE system with self-diffusion. With the presence of the cross-diffusion, the homogeneous equilibrium is destabilized, and a heterogenous steady-state emerges as a consequence. In addition, the conditions guaranteeing the emergence of Turing patterns are derived.

AB - In this paper, we consider a sex-structured predator-prey model with strongly coupled nonlinear reaction diffusion. Using the Lyapunov functional and Leray-Schauder degree theory, the existence and stability of both homogenous and heterogenous steady-states are investigated. Our results demonstrate that the unique homogenous steady-state is locally asymptotically stable for the associated ODE system and PDE system with self-diffusion. With the presence of the cross-diffusion, the homogeneous equilibrium is destabilized, and a heterogenous steady-state emerges as a consequence. In addition, the conditions guaranteeing the emergence of Turing patterns are derived.

KW - Predator-prey model

KW - Cross-diffusion

KW - Turing pattern

KW - Sex structure

U2 - 10.1142/S179352451100157X

DO - 10.1142/S179352451100157X

JO - International Journal of Biomathematics

JF - International Journal of Biomathematics

SN - 1793-5245

IS - 4

VL - 5

ER -