Spatiotemporal dynamics for a Belousov–Zhabotinsky reaction–diffusion system with nonlocal effects

Abstract

This paper is devoted to study the dynamical behavior of a Belousov–Zhabotinsky reaction–diffusion system with nonlocal effect and find the essential difference between it and classical equations. First, we prove the existence of the solution by using the comparison principle and constructing monotonic sequences. Furthermore, the uniqueness is given by using fundamental solution and Gronwall's inequality. Then we obtain the uniform boundedness of the solution by means of auxiliary function. Finally, we investigate the states of the solution as the parameters change and show some new and interesting phenomena about nonlocal Belousov–Zhabotinsky reaction–diffusion system by using stability analysis and numerical simulations.

Keywords:

• Belousov–Zhabotinsky reaction
• nonlocal
• existence
• uniqueness
• numerical simulation

2010 AMS Subject Classifications:

• 35A01
• 35K55
• 35K57
• 92D25

Acknowledgements

This work was supported by NSF of China (11801470) and the Fundamental Research Funds for the Central Universities (2682018CX64).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by NSF of China (11801470) and the Fundamental Research Funds for the Central Universities(2682018CX64).