Abstract
In this paper, the quasi-projective synchronization of distributed-order recurrent neural networks is investigated. Firstly, based on the definition of the distributed-order derivative and metric space theory, two distributed-order differential inequalities are obtained. Then, by employing the Lyapunov method, Laplace transform, Laplace final value theorem, and some inequality techniques, the quasi-projective synchronization sufficient conditions for distributed-order recurrent neural networks are established in cases of feedback control and hybrid control schemes, respectively. Finally, two numerical examples are given to verify the effectiveness of the theoretical results.
Highlights
Fractional calculus has more merits than classical integer-order calculus in the description of memory and hereditary properties for a variety of materials and processes, and has been of great interest to scholars [1,2]
As a general rule of fractional calculus, the distributed-order derivative was proposed by Caputo [9]
It is worth noting that a distributed-order derivative is more accurate in describing and explaining some physical phenomena, such as networked structures, the complexity of nonlinear systems, non-homogeneous, multi-scale, and multi-spectral phenomena [10,11,12,13]
Summary
Fractional calculus has more merits than classical integer-order calculus in the description of memory and hereditary properties for a variety of materials and processes, and has been of great interest to scholars [1,2]. In [27], the authors proposed a fractional-order recurrent neural network sliding mode control scheme for a class of dynamic systems. Motivated by the above discussions, in this paper, we investigate the quasi-projective synchronization of distributed-order recurrent neural networks. By applying the feedback control, the quasi-projective synchronization of distributed-order recurrent neural networks are obtained. The quasi-projective synchronization of distributed-order recurrent neural networks are investigated in the case of a hybrid control scheme. (3) Several sufficient criteria for quasi-projective synchronization of distributed-order recurrent neural networks are established. We deduced some necessary lemmas and some results that conduce to establish sufficient conditions for the quasi-projective synchronization of distributed-order recurrent neural networks.
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