Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

Abstract

This paper investigates the existence and globally asymptotic stability of equilibrium solution for Riemann-Liouville fractionalorder hybrid BAM neural networks with distributed delays and impulses. The factors of such network systems including the distributed delays, impulsive effects, and two different fractional-order derivatives between the -layer and -layer are taken into account synchronously. Based on the contraction mapping principle, the sufficient conditions are derived to ensure the existence and uniqueness of the equilibrium solution for such network systems. By constructing a novel Lyapunov functional composed of fractional integral and definite integral terms, the globally asymptotic stability criteria of the equilibrium solution are obtained, which are dependent on the order of fractional derivative and network parameters. The advantage of our constructed method is that one may directly calculate integer-order derivative of the Lyapunov functional. A numerical example is also presented to show the validity and feasibility of the theoretical results.

Mean-square stability of Riemann–Liouville fractional Hopfield’s graded response neural networks with random impulses

“…equaling to values of the state variable after the jump and before the jump, respectively, or similar one. In the case of the RL fractional derivative, some authors use this type of impulsive conditions (see, for example, [28]). But because of the type of the initial condition, we think that the above given type of the impulsive condition is not appropriate.…”

“…In the case when the time of impulsive perturbations are initially given deterministic points, the impulsive models with ordinary derivatives for neural networks are studied in [9,19,22,25,26,33]. Note that impulsive fractional neural networks are studied for Caputo fractional derivative in several papers, such as [17,20,24,32], and for RL fractional derivative, see [28,29].…”

Hybrid Control Scheme for Projective Lag Synchronization of Riemann–Liouville Sense Fractional Order Memristive BAM NeuralNetworks with Mixed Delays

“…Otherwise, during a particular period, the signal propagation is distributed because the variety of axon sizes and lengths are too large. In this manner, the attention of distributed delays is significant in fractional order neural networks (FONNs) dynamical systems, and there is a huge amount of research works on FONNs with distributed delay-see, for instance, [35,36]. In [20], the existence and Lyapunov-stability of impulsive hybrid FOBNNs with mixed delays were discussed by Zhang et al and the sufficient conditions are derived to assure the stability condition of Hybrid FOBNNs with mixed time-delays via contraction mapping principle, integer order Lyapunov functional and periodically intermittent control.…”

Stability Analysis of Fractional‐Order Bidirectional Associative Memory Neural Networks with Mixed Time‐Varying Delays

“…In recent years, many great contributions have been made to the dynamics of systems [11][12][13][14][15][16][17][18][19][20][21][22] which is closely related to the applications in various elds. For example, the references [11,[14][15][16][17][18][19][20] reported some research on the global asymptotic stability, Mittag-Le er stability, uniform stability, and nite-time stability. In [12,21,22], the authors investigated the adaptive synchronization, the nite-time synchronization, and the Mittag-Le er synchronization for several kinds of fractional-order BAM neural networks.…”