Strong convergence and almost sure exponential stability of balanced numerical approximations to stochastic delay Hopfield neural networks

Rathinasamy, A.; Mayavel, Pichamuthu

doi:10.1016/j.amc.2022.127573

Cited by 7 publications

(1 citation statement)

References 27 publications

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“…Currently, NNs are successfully applied to optimization calculation, automatic control, signal processing, and secure communication [1]. At the same time, many important NN models have been presented by means of the first-order differential equations, including Hopfield NNs [2], competitive NNs [3], cellular NNs [4], and bidirectional associative memory (BAM) NNs [5]. However, it was revealed that NNs depicted as the first-order systems cannot effectively simulate the working mechanism of squid semicircular canal and synapse [6].…”

Section: Introductionmentioning

confidence: 99%

Stability and Synchronization of Fractional-Order Complex-Valued Inertial Neural Networks: A Direct Approach

Song¹,

Yu²

2022

Mathematics

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This paper is dedicated to the asymptotic stability and synchronization for a type of fractional complex-valued inertial neural network by developing a direct analysis method. First, a new fractional differential inequality is presented for nonnegative functions, which provides an effective tool for the convergence analysis of fractional-order systems. Moreover, instead of the previous separation analysis for complex-valued neural networks, a class of Lyapunov functions composed of the complex-valued states and their fractional derivatives is constructed, and some compact stability criteria are derived. In synchronization analysis, unlike the existing control schemes for reduced-order subsystems, some feedback and adaptive control schemes, formed by the linear part and the fractional derivative part, are directly designed for the response fractional inertial neural networks, and some synchronization conditions are derived using the established fractional inequality. Finally, the theoretical analysis is supported via two numerical examples.

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