New type of the source of travelling impulses in two-variable model of reaction–diffusion system

Abstract

A two-variable model of a one-dimensional, open, excitable, finite reaction-diffusion system describing time-space evolution of traveling impulses is investigated. It is shown that depending on the size of the system, the traveling impulse after reflection can generate either a source of decaying traveling impulses or a stationary periodical structure. A continuous increase of the size of the system causes periodical repetitions of these patterns. The chemical model is realistic and can become a stimulus for seeking the described effect in experiments.

Modeling Studies of Inhomogeneity Effects during Laser Flash Photolysis Experiments: A Reaction–Diffusion Approach

“…A reaction–diffusion partial differential equation is set up and solved in order to model the processes in a LFP experiment. Inspired by the seminal work of Alan Turing on morphogenesis (shape formation in biological systems), reaction–diffusion systems have already proved very useful in interpreting chemical and biological pattern formation − as well as other nonlinear dynamic phenomena such as oscillation, chaos, or self-organizing systems up to the most recent literature studies. − …”

Editorial

“…It was shown experimentally that transitions between Turing patterns and uniform oscillations are possible. Moreover, a simulation of traveling impulses was explored by Kawczińsky et al [9]. A model of the enzymatic transformations was used in this case study.…”