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Spatial pattern formation driven by the cross-diffusion in a predator–prey model with Holling type functional response.
- Source :
-
Chaos, Solitons & Fractals . Sep2023, Vol. 174, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- In this paper, we consider a cross-diffusion predator–prey system with Holling type functional response. We study the local stability, Turing instability, spatial pattern formation, Hopf and Turing–Hopf bifurcation of the equilibrium. Numerical simulation with zero-flux boundary conditions discloses that the system under consideration experiences the occurrence of cross-diffusion-driven instability. The dynamical system in Turing space emerges spots, stripe-spot mixtures and labyrinthine patterns, which reveals that the interaction of both self- and cross-diffusions play a significant role on the pattern formation of the present system in a way to enrich the pattern. We obtain the normal form of the Turing–Hopf bifurcation and observe that the system has stably spatially homogeneous periodic solutions, stable constant and nonconstant steady-state solutions, which indicates that the intrinsic growth rate coefficient and the environmental carrying capacity coefficient are two important factors for predator–prey system, and affect the stability of predator–prey system. • A cross-diffusion predator–prey system with habitat complexity and Holling type functional response is considered. • The Turing pattern is studied by the amplitude equation. • The Turing–Hopf bifurcation is investigated by using the method of the normal form and the center manifold theory. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PREDATION
*HOPF bifurcations
*DYNAMICAL systems
*COMPUTER simulation
Subjects
Details
- Language :
- English
- ISSN :
- 09600779
- Volume :
- 174
- Database :
- Academic Search Index
- Journal :
- Chaos, Solitons & Fractals
- Publication Type :
- Periodical
- Accession number :
- 171312037
- Full Text :
- https://doi.org/10.1016/j.chaos.2023.113890