Research article

Spatio-temporal Bazykin’s model with space-time nonlocality

  • Received: 06 May 2020 Accepted: 08 July 2020 Published: 10 July 2020
  • This work deals with a reaction-diffusion model for prey-predator interaction with Bazykin's reaction kinetics and a nonlocal interaction term in prey growth. The kernel of the integral characterizes nonlocal consumption of resources and depends on space and time. Linear stability analysis determines the conditions of the emergence of Turing patterns without and with nonlocal term, while weakly nonlinear analysis allows the derivation of amplitude equations. The bifurcation analysis and numerical simulation carried out in this work reveal the existence of stationary and dynamic patterns appearing due to the loss of stability of the coexistence homogeneous steady-state.

    Citation: Swadesh Pal, Malay Banerjee, Vitaly Volpert. Spatio-temporal Bazykin’s model with space-time nonlocality[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4801-4824. doi: 10.3934/mbe.2020262

    Related Papers:

  • This work deals with a reaction-diffusion model for prey-predator interaction with Bazykin's reaction kinetics and a nonlocal interaction term in prey growth. The kernel of the integral characterizes nonlocal consumption of resources and depends on space and time. Linear stability analysis determines the conditions of the emergence of Turing patterns without and with nonlocal term, while weakly nonlinear analysis allows the derivation of amplitude equations. The bifurcation analysis and numerical simulation carried out in this work reveal the existence of stationary and dynamic patterns appearing due to the loss of stability of the coexistence homogeneous steady-state.
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    © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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