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Competitive neural networks(CNNs) has not been well developed in nonlinear fractional order dynamical system, which is developed first time in this paper. Then, by means of a proper Lyapunov functional, asymptotic expansion of Mittag-Leffler function properties, together with some Caputo derivative properties, the testable novel sufficient conditions are given to guarantee the existence, uniqueness of the equilibrium point as well as global asymptotic stability for a class of fractional order competitive neural networks (FOCNNs) are all derived in the form of matrix elements. Furthermore, the boundedness for the solution of FOCNN is presented by employing Cauchy–Schwartz inequality and Gronwall inequality. Besides, a linear feedback control and adaptive feedback control are designed to achieve the global asymptotic synchronization criterion for FOCNNs with time delay and these explored consequences are extended from some previous integer order CNNs output. At last, two numerical simulations are performed to illustrate the effectiveness of our proposed theoretical results.

In this paper, the asymptotic stability analysis is investigated for a kind of discrete-time bidirectional associative memory (BAM) neural networks with the existence of perturbations namely, stochastic, Markovian jumping and impulses. Based on the theory of stability, a novel Lyapunov–Krasovskii function is constructed and by utilizing the concept of delay partitioning approach, a new linear-matrix-inequality (LMI) based criterion for the stability of such a system is proposed. Furthermore, the derived sufficient conditions are expressed in the structure of LMI, which can be easily verified by a known software package that guarantees the globally asymptotic stability of the equilibrium point. Eventually, a numerical example with simulation is given to demonstrate the effectiveness and applicability of the proposed method.

In this paper, the stability analysis of impulsive discrete-time stochastic BAM neural networks with leakage and mixed time delays is investigated via some novel Lyapunov–Krasoviskii functional terms and effective techniques. For the target model, stochastic disturbances are described by Brownian motion. Then the result is further extended to address the problem of robust stability of uncertain discrete-time BAM neural networks. The conditions obtained here are expressed in terms of Linear Matrix Inequalities (LMIs), which can be easily checked by MATLAB LMI control toolbox. Finally, few numerical examples are presented to substantiate the effectiveness of the derived LMI-based stability conditions.

In this paper, the global robust exponential stability problem for a class of uncertain inertial-type BAM neural networks with both time-varying delays is focused through Lagrange sense. The existence of time-varying delays in discrete and distributed terms is explored with the availability of lower and upper bounds of time-varying delays. Firstly, we transform the proposed inertial BAM neural networks to usual one. Secondly, by the aid of LKF, stability theory, integral inequality, some novel sufficient conditions for the global robust exponential stability of the addressed neural networks are obtained in terms of linear matrix inequalities, which can be easily tested in practice by utilizing LMI control toolbox in MATLAB software. Furthermore, many comparisons of proposed work are listed with some existing literatures to get less conservatism. Finally, two numerical examples are provided to demonstrate the advantages and superiority of our theoretical outcomes.

In this work, we probes the stability results of H∞ state estimation for discrete-time stochastic genetic regulatory networks with leakage, distributed delays, Markovian jumping parameters and impulsive effects. Here, we focus to evaluate the true absorption of mRNAs and proteins by calculating the H∞ estimator in such a way that the estimation error dynamics is stochastically stable during the completion of the prescribed H∞ disturbance attenuation level. In favor of decreasing the data communion in trouble, the H∞ system accept and evaluate the outputs that are only transferred to the estimator when a certain case is acroses. Further, few sufficient conditions are formulated, by utilizing the Lyapunov–Krasovskii functional under which the estimation error system is stochastically stable and also satisfied the H∞ attainment constraint. The estimator is obtained in terms of linear matrix inequalities (LMIs) and these LMIs are attainable, only if the estimator gains can be absolutely given. In addition to that, two numerical examples are exposed to establish the efficiency of our obtained results.