Abstract
In this paper, a fractional-order Cohen–Grossberg-type neural network with Caputo fractional derivatives is investigated. The notion of almost periodicity is adapted to the impulsive generalization of the model. General types of impulsive perturbations not necessarily at fixed moments are considered. Criteria for the existence and uniqueness of almost periodic waves are proposed. Furthermore, the global perfect Mittag–Leffler stability notion for the almost periodic solution is defined and studied. In addition, a robust global perfect Mittag–Leffler stability analysis is proposed. Lyapunov-type functions and fractional inequalities are applied in the proof. Since the type of Cohen–Grossberg neural networks generalizes several basic neural network models, this research contributes to the development of the investigations on numerous fractional neural network models.
Highlights
Fractional-order differential systems have attracted a lot of attention in research since fractional-order derivatives are distinguished by its substantial degree of reliability and accuracy
Since more and more experimental results show that real-world models follow fractional calculus dynamics, very recently fractional-order differential systems are successfully applied in various fields of science and engineering [9,10], including COVID-19 models [11]
As we can see from the presented examples, the proposed impulsive control technique may be efficiently applied in the global perfect Mittag–Leffler stability analysis of the almost periodic solutions
Summary
Fractional-order differential systems have attracted a lot of attention in research since fractional-order derivatives are distinguished by its substantial degree of reliability and accuracy. The research on the theory and applications of the Cohen–Grossberg-type neural networks with fractional-order derivatives still needs more development. Many researchers investigated the impulsive effects on the fundamental and qualitative properties of fractional-order models [25,26,27], including numerous fractional neural network models [28,29,30,31]. The main purpose of this study is to contribute to the development of the theory of almost periodicity for such classes of impulsive fractional neural network models. For integer-order Cohen–Grossberg neural networks under impulsive perturbations, the almost periodicity is studied in very few papers [38,40,45,46].
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