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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Bifurcation and spatiotemporal patterns in a Bazykin predator-prey model with self and cross diffusion and Beddington-DeAngelis response

Pages: 717 - 740, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017035

 
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Eric Avila-Vales - Facultad de Matemáticas, Universidad Autónoma de Yucatán, Anillo Periférico Norte, Tablaje 13615, C.P. 97119, Mérida, Mexico (email)
Gerardo García-Almeida - Facultad de Matemáticas, Universidad Autónoma de Yucatán, Anillo Periférico Norte, Tablaje 13615, C.P. 97119, Mérida, Mexico (email)
Erika Rivero-Esquivel - Facultad de Matemáticas, Universidad Autónoma de Yucatán, Anillo Periférico Norte, Tablaje 13615, C.P. 97119, Mérida, Mexico (email)

Abstract: In this article, the clasical Bazykin model is modifed with Bedding--ton--DeAngelis functional response, subject to self and cross-diffusion, in order to study the spatial dynamics of the model.We perform a detailed stability and Hopf bifurcation analysis of the spatial model system and determine the direction of Hopf bifurcation and stability of the bifurcating periodic solutions. We present some numerical simulations of time evolution of patterns to show the important role played by self and cross-diffusion as well as other parameters leading to complex patterns in the plane.

Keywords:  Cross-diffusion, Turing instability, Hopf bifurcation, Turing pattern, Beddington-DeAngelis response.
Mathematics Subject Classification:  Primary: 35B32, 35B35, 35B36; Secondary: 35Q92.

Received: August 2015;      Revised: June 2016;      Available Online: December 2016.

 References