Open AccessSpatio-temporal Bazykin’s model with space-time nonlocality
Author(s) -
Swadesh Pal,
Malay Banerjee,
Vitaly Volpert
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020262
Subject(s) - quantum nonlocality , nonlinear system , statistical physics , stability (learning theory) , mathematics , term (time) , work (physics) , kernel (algebra) , reaction–diffusion system , hopf bifurcation , turing , mathematical analysis , bifurcation , classical mechanics , physics , computer science , pure mathematics , quantum mechanics , machine learning , quantum entanglement , quantum , thermodynamics , programming language
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.