The Normal Velocity of the Population Front in the “Predator–Prey” Model

¹ Laboratory of Computational Informatics, Institute of Applied mathematics FEB RAS, 69041 Vladivostok, Russia
² Department of Mathematics and Modelling, Vladivostok State University of Economics and Service, 69014 Vladivostok, Russia
³ Laboratory of Nonlinear Dynamics and Theoretical Biophysics, P.N. Lebedev Physical Institute RAS, 119991 Moscow, Russia
⁴ Institute of Fluid Science, Tohoku University, Sendai, Japan

^* Corresponding author: datsep@gmail.com

Received: 5 September 2021
Accepted: 10 August 2022

Abstract

The propagation of one and two-dimensional waves of populations are numerically investigated in the framework of the “predator-prey” model with the Arditi - Ginzburg trophic function. The propagation of prey and predator population waves and the propagation of co-existing populations’ waves are considered. The simulations demonstrate that even in the case of an unstable quasi-equilibrium state of the system, which is established behind the front of a traveling wave, the propagation velocity of the joint population wave is a well-defined function. The calculated average propagation velocity of a cellular non-stationary wave front is determined uniquely for a given set of problem parameters. The estimations of the wave propagation velocity are obtained for both the case of a plane and cellular wave fronts of populations. The structure and velocity of outward propagating circular cellular wave are investigated to clarify the local curvature and scaling effects on the wave dynamics.