Almost periodic dynamics in a new class of impulsive reaction–diffusion neural networks with fractional-like derivatives. (February 2021)

• Record Type: Journal Article
• Authors: Stamov, Gani; Stamova, Ivanka; Martynyuk, Anatoliy; Stamov, Trayan
• Is Part Of: Chaos, solitons and fractals. Volume 143(2021)
• Publication Date: 2021-02
• Subjects: Almost periodicity -- Fractional-like derivatives -- HBV infection -- Impulses -- Reaction-diffusion neural networks; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110647
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: This paper introduces a new class of reaction–diffusion neural networks with impulses and recently defined fractional-like derivatives. Sufficient conditions for the existence-uniqueness of almost periodic solutions are proposed by constructing suitable Lyapunov-like functions. Our results are new and contribute to the development of the knowledge on impulsive fractional-like evolution models. Finally, as an example a fractional-like generalization of a reaction-diffusion model in epidemiology that simulates the hepatitis B virus (HBV) infection with spatial dependence is considered.