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Turing instability for a competitor-competitor-mutualist model with nonlinear cross-diffusion effects

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  • Wen, Zijuan
  • Fu, Shengmao

Abstract

This paper deals with a strongly coupled reaction-diffusion system modeling a competitor-competitor-mutualist three-species model with diffusion, self-diffusion and nonlinear cross-diffusion and subject to Neumann boundary conditions. First, we establish the persistence of a corresponding reaction-diffusion system without self- and cross-diffusion. Second, the global asymptotic stability of the unique positive equilibrium for weakly coupled PDE system is established by using a comparison method. Moreover, under certain conditions about the intra- and inter-species effects, we prove that the uniform positive steady state is linearly unstable for the cross-diffusion system when one of the cross-diffusions is large enough. The results indicate that Turing instability can be driven solely from strong diffusion effect of the first species (or the second species or the third species) due to the pressure of the second species (or the first species).

Suggested Citation

  • Wen, Zijuan & Fu, Shengmao, 2016. "Turing instability for a competitor-competitor-mutualist model with nonlinear cross-diffusion effects," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 379-385.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:379-385
    DOI: 10.1016/j.chaos.2016.06.019
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    References listed on IDEAS

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    1. Shengmao Fu & Lina Zhang, 2012. "Instability Induced by Cross-Diffusion in a Predator-Prey Model with Sex Structure," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, March.
    2. Guin, Lakshmi Narayan, 2015. "Spatial patterns through Turing instability in a reaction–diffusion predator–prey model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 174-185.
    3. Zhang, Jia-Fang & Chen, Heshan, 2014. "Global asymptotic behavior in a Lotka–Volterra competition system with spatio-temporal delays," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 69-75.
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    Cited by:

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