Work

CMMSE: New Properties of Auto‐Wave Solutions in Activator‐Inhibitor Reaction‐Diffusion Systems With Fractional Derivatives

Year: 2024

Type: article

Abstract: ABSTRACT In this article, we analyze new properties of auto‐wave solutions in fractional reaction‐diffusion systems. These new properties arise due to a change in fractional derivative order and do not occur in systems with classical derivatives. It is shown that the stability of steady‐state solutions and their evolution are mainly determined by the eigenvalue spectrum of a linearized system and the fractional derivative order. It is also demonstrated that the basic properties of auto‐wave solutions in fractional‐order systems can essentially differ from those in standard systems. The results of the linear stability analysis are confirmed by computer simulations of the generalized fractional van der Pol–FitzHugh–Nagumo mathematical model. A common picture of possible instabilities and auto‐wave solutions in time‐fractional two‐component activator‐inhibitor systems is presented.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.10672

Authors: Bohdan Datsko, Vasyl Gafiychuk

Institutions: Rzeszów University of Technology, National Academy of Sciences of Ukraine

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W4405765024

FWCI: 0.169

Cites: 30

Cited by: 1

Related to: 10