Investigation into the Critical Domain Problem for the Reaction-Telegraph Equation Using Advanced Numerical Algorithms

Abstract

Reaction-telegraph equation (RTE)—a nonlinear partial differential equation of mixed parabolic-hyperbolic type—is believed to be a better mathematical framework to describe population dynamics than the more traditional reaction–diffusion equations. Being motivated by ecological problems such as habitat fragmentation and alien species introduction (biological invasions), here we consider the RTE on a bounded domain with the goal to reveal the dependence of the critical domain size (that separates extinction from persistence) on biologically meaningful parameters of the equation. Since an analytical study does not seem to be possible, we investigate into this critical domain problem by means of computer simulations using an advanced numerical algorithm. We show that the population dynamics described by the RTE is significantly different from those of the corresponding reaction–diffusion equation. The properties of the critical domain are revealed accordingly.