Abstract
This paper investigates the quasi-synchronization of nonidentical fractional-order memristive neural networks (FMNNs) via impulsive control. Based on a newly provided fractional-order impulsive systems comparison lemma, the average impulsive interval definition, and the Laplace transform, some quasi-synchronization conditions are obtained with fractional order 0 < α < 1 . In addition, the error convergence rates and error boundary are also obtained. Finally, one simulation example is presented to show the validity of our results.
Highlights
Memristor was predicted as the fourth circuit element describing the relationship between magnetic flux and voltage by professor Chua [1] in 1971. is component was established successfully by HP Laboratories [2, 3] in 2008
Fractional calculus originated in the 17th century and is a generalization of integer-order calculus operations to arbitrary order calculus operations [13]
fractional-order memristive neural networks (FMNNs) can describe the memory properties of neurons more accurately and achieve many results in synchronization and stability [17,18,19,20]. e global Mittag–Leffler stabilization of a class of FMNNs with time delays was discussed under a state feedback control in [17]
Summary
Memristor was predicted as the fourth circuit element describing the relationship between magnetic flux and voltage by professor Chua [1] in 1971. is component was established successfully by HP Laboratories [2, 3] in 2008. Memristors are used instead of traditional resistive elements to simulate brain neuron synapses and build the memristor neural networks (MNNs) model [4,5,6,7,8,9] because they have memory characteristics. It has been widely used in the field of information processing, associative memory, and image processing [10,11,12]. The impulsive control method has been widely used in the quasi-synchronization of chaotic systems He et al used a distributed impulsive control studying the quasi-synchronization problem of drive-response heterogeneous networks in [21] and the number of controlled nodes was considered. Define χ(t) as a continuous function except at some finite number of points tk at which χ(t+k ) χ(tk) and χ(t−k ) exist; the set of piecewise right continuous function χ(t) is defined as PC(l) χ|χ: [−τ, ∞) ⟶ Rl
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