On boundedness and projective synchronization of distributed order neural networks

Gamal M. Mahmoud, Tarek Aboelenen, Tarek M. Abed-Elhameed and Ahmed A. Farghaly

Applied Mathematics and Computation, 2021, vol. 404, issue C

Abstract: In this work, we introduced the distributed-order neural networks (DONNs) which are the generalization of integer and fractional orders neural networks. We presented and proved two theorems for bounded solutions and solutions that approach zero of these networks. The Gronwall–Bellman lemma, the asymptotical expansion of the generalized Mittag–Leffler function and Laplace transform are used to prove these theorems. We derived analytically the condition under which the solution of this network (DONN) is bounded. The active control and Lyapunov direct methods are applied to study the projective synchronization between two different chaotic DONNs. The analytical control functions are derived to achieve our synchronization. Two different examples of DONNs are given to test the validity of the analytical results of our theorems. The projective synchronization is investigated. Numerical simulations are implemented to show the agreement between both analytical and numerical results.

Keywords: Distributed order; Neural networks; Mittag–-Leffler function; Chaos synchronization (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:404:y:2021:i:c:s0096300321002885

DOI: 10.1016/j.amc.2021.126198

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