Stationary And Time-Periodic Patterns Of Two-Predator And One-Prey Systems With Prey-Taxis

Keywords

Pattern formation; Predator-prey model; Prey-taxis; Stability analysis; Stationary solutions; Time-periodic solutions

Abstract

This paper concerns pattern formation in a class of reaction-advection-diffusion systems modeling the population dynamics of two predators and one prey. We consider the biological situation that both predators forage along the population density gradient of the preys which can defend themselves as a group. We prove the global existence and uniform boundedness of positive classical solutions for the fully parabolic system over a bounded domain with space dimension N = 1; 2 and for the parabolic-parabolic-elliptic system over higher space dimensions. Linearized stability analysis shows that prey-taxis stabilizes the positive constant equilibrium if there is no group defense while it destabilizes the equilibrium otherwise. Then we obtain stationary and time-periodic nontrivial solutions of the system that bifurcate from the positive constant equilibrium. Moreover, the stability of these solutions is also analyzed in detail which provides a wave mode selection mechanism of nontrivial patterns for this strongly coupled system. Finally, we perform numerical simulations to illustrate and support our theoretical results.

Publication Date

1-1-2017

Publication Title

Discrete and Continuous Dynamical Systems- Series A

Volume

37

Issue

1

Number of Pages

505-543

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.3934/dcds.2017021

Socpus ID

84995794401 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84995794401

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