Finite-time H∞ output synchronization for DCRDNNs with multiple delayed and adaptive output couplings

This work concentrates on solving the finite-time H∞ output synchronization (FTHOS) issue of directed coupled reaction-diffusion neural networks (DCRDNNs) with multiple delayed and adaptive output couplings in the presence of external disturbances. Based on the output information, an adaptive law to adjust output coupling weights and a controller are respectively developed to ensure that the DCRDNNs achieve FTHOS. Then, in the special case of no external disturbances, a corollary on the finite-time output synchronization (FTOS) of the DCRDNNs with multiple delayed and adaptive output couplings is provided. In addition, a novel adaptive scheme to update output coupling weights is devised to ensure H∞ output synchronization (HOS) in the DCRDNNs with multiple delayed output couplings. Finally, the relevant simulation graphs are provided to certify the validity of several synchronization criteria.

New delay-dependent uniform stability criteria for fractional-order BAM neural networks with discrete and distributed delays

Initially, a class of Caputo fractional-order bidirectional associative memory neural networks in two variables is developed, building upon the groundwork laid by delayed Caputo fractional system in one variable. Next, the Razumikhin-type uniform stability conditions, originally formulated for single-variable systems, are successfully extended to accommodate the complexities of delayed Caputo fractional systems in two variables. Leveraging this extension and employing a suitable Lyapunov function, the delay-dependent uniform stability criteria for the addressed fractional-order bidirectional associative memory neural networks are expressed in terms of linear matrix inequalities. Finally, the effectiveness and practicality of the theoretical findings are demonstrated through the application of two numerical examples, affirming the viability of the proposed approach.

Bifurcations of a delayed fractional-order BAM neural network via new parameter perturbations

This paper makes a new breakthrough in deliberating the bifurcations of fractional-order bidirectional associative memory neural network (FOBAMNN). In the beginning, the corresponding bifurcation results are established according to self-regulating parameter, which is different from bifurcation outcomes available by using time delay as the bifurcation parameter, and greatly enriches the bifurcation results of continuous neural networks(NNs). The deived results manifest that a larger self-regulating parameter is more conducive to the stability of the system, which is consistent with the actual meaning of the self-regulating parameter representing the decay rate of activity. In addition to the innovation in the research object, this paper also has innovation in the procedure of calculating the bifurcation critical point. In the face of the quartic equation about the bifurcation parameters, this paper utilizes the methodology of implicit array to calculate the bifurcation critical point succinctly and effectively, which eschews the disadvantages of the conventional Ferrari approach, such as cumbersome formula and huge computational efforts. Our developed technique can be employed as a general method to solve the bifurcation point including the problem of dealing with the bifurcation critical point of delay. Ultimately, numerical experiments test the key theoretical fruits of this paper.

A new predefined-time stability theorem and its application in the synchronization of memristive complex-valued BAM neural networks

In this paper, two novel and general predefined-time stability lemmas are given and applied to the predefined-time synchronization problem of memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs). Firstly, different from the generally fixed-time stability lemma, the setting of an adjustable time parameter in the derived predefined-time stability lemma causes it to be more flexible and more general. Secondly, the model studied in the complex-valued BAM neural networks model, which is different from the previous discussion of the real part and imaginary part respectively. It is more practical to study the complex-valued nonseparation. Thirdly, two effective controllers are designed to realize the synchronization performance of BAM neural networks based on the predefined-time stability, and the analysis is given based on general predefined-time synchronization. Finally, the correctness of the theoretical derivation is verified by numerical simulation. A secure communication scheme based on predefined-time synchronization of MCVBAMNNs is proposed, and the effectiveness and superiority of the results are proved.

Global Stability of Bidirectional Associative Memory Neural Networks With Multiple Time-Varying Delays

This article investigates the global stability of bidirectional associative memory neural networks with discrete and distributed time-varying delays (DBAMNNs). By employing the comparison strategy and inequality techniques, global asymptotic stability (GAS) and global exponential stability (GES) of the underlying DBAMNNs are of concern in terms of p -norm ( p ≥ 2 ). Meanwhile, GES of the addressed DBAMNNs is also analyzed in terms of 1-norm. When distributed time delay is neglected, the GES of the corresponding bidirectional associative memory neural networks is presented as an M -matrix, which includes certain existing outcomes as special cases. Two examples are finally provided to substantiate the validity of theories.

Quantization synchronization of chaotic neural networks with time delay under event-triggered strategy

This paper shows solicitude for the quantization synchronization of delayed chaotic master and slave neural networks under an dynamic event-triggered strategy. In virtue of a generalized Halanay-type inequality, a theoretical criterion for quasi-synchronization of master and slave neural networks is derived. Meanwhile, we can obtain an exact upper bound of synchronization error by using this criterion. Compared with output feedback controller with event triggering and quantization, the case where the controller only affected by quantization is also considered. Then, we exclude the Zeno behavior of the event-triggered controller. A sufficient criterion for the existence of the quantized output feedback controllers is also provided. A numerical example is cited to illustrate the efficiency of our theoretical criteria. In addition, some experiments of secure image communication are conducted under quasi-synchronization of master and slave neural networks.

Producing Stable Periodic Solutions of Switched Impulsive Delayed Neural Networks Using a Matrix-Based Cubic Convex Combination Approach

This article is dedicated to designing a novel periodic impulsive control strategy for producing globally exponentially stable periodic solutions for switched neural networks with discrete and finite distributed time-varying delays. First, tunable parameters and cubic convex combination approach are proposed to study the globally exponential convergence of switched neural networks. Second, a sufficient criterion for the existence, uniqueness, and globally exponential stability of a periodic solution is demonstrated by using contraction mapping theorem and the impulse-delay-dependent Lyapunov-Krasovskii functional method. It is worth emphasizing that the addressed Lyapunov-Krasovskii functional covers both triple integral terms and novel quadruple integral terms, which makes the conservatism of the above criteria decrease. Even if the original neural network models are unstable or the impulsive effects are strong, the addressed neural network model can produce a globally exponentially stable periodic solution. These results here, which include boundedness, globally uniformly exponential convergence, and globally exponentially stability of the periodic solution, generalize and improve the earlier publications. Finally, two numerical examples and their computer simulations are given to show the effectiveness of theoretical results.

Monostability and Multistability for Almost-Periodic Solutions of Fractional-Order Neural Networks With Unsaturating Piecewise Linear Activation Functions

Since the unsaturating activation function is unbounded, more complex dynamics may exist in neural networks with this kind of activation function. In this article, monostability and multistability results of almost-periodic solutions are developed for fractional-order neural networks with unsaturating piecewise linear activation functions. Some globally Mittag-Leffler attractive sets are given, and the existence of globally Mittag-Leffler stable almost-periodic solution is demonstrated by using Ascoli-Arzela theorem. In particular, some sufficient conditions are provided to ascertain the multistability of almost-periodic solutions based on locally positively invariant set. It shows that there exists an almost-periodic solution in each positively invariant set, and all trajectories converge to this periodic trajectory in that rectangular area. Two illustrative examples are provided to demonstrate the effectiveness of the proposed sufficient criteria.

A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks

In this paper, we derive a new fixed-time stability theorem based on definite integral, variable substitution and some inequality techniques. The fixed-time stability criterion and the upper bound estimate formula for the settling time are different from those in the existing fixed-time stability theorems. Based on the new fixed-time stability theorem, the fixed-time synchronization of neural networks is investigated by designing feedback controller, and sufficient conditions are derived to guarantee the fixed-time synchronization of neural networks. To show the usability and superiority of the obtained theoretical results, we propose a secure communication scheme based on the fixed-time synchronization of neural networks. Numerical simulations illustrate that the new upper bound estimate formula for the settling time is much tighter than those in the existing fixed-time stability theorems. Moreover, the plaintext signals can be recovered according to the new fixed-time stability theorem, while the plaintext signals cannot be recovered according to the existing fixed-time stability theorems.

Effects of variable-time impulses on global exponential stability of Cohen–Grossberg neural networks

We investigate the global exponential stability of Cohen–Grossberg neural networks (CGNNs) with variable moments of impulses using B-equivalence method. Under certain conditions, we show that each solution of the considered system intersects each surface of discontinuity exactly once, and that the variable-time impulsive systems can be reduced to the fixed-time impulsive ones. The obtained results imply that impulsive CGNN will remain stability property of continuous subsystem even if the impulses are of somewhat destabilizing, and that stabilizing impulses can stabilize the unstable continuous subsystem at its equilibrium points. Moreover, two stability criteria for the considered CGNN by use of proposed comparison system are obtained. Finally, the theoretical results are illustrated by two examples.

Pinning Impulsive Synchronization of Reaction-Diffusion Neural Networks With Time-Varying Delays

This paper investigates the exponential synchronization of reaction-diffusion neural networks with time-varying delays subject to Dirichlet boundary conditions. A novel type of pinning impulsive controllers is proposed to synchronize the reaction-diffusion neural networks with time-varying delays. By applying the Lyapunov functional method, sufficient verifiable conditions are constructed for the exponential synchronization of delayed reaction-diffusion neural networks with large and small delay sizes. It is shown that synchronization can be realized by pinning impulsive control of a small portion of neurons of the network; the technique used in this paper is also applicable to reaction-diffusion networks with Neumann boundary conditions. Numerical examples are presented to demonstrate the effectiveness of the theoretical results.

C1-almost periodic solutions of BAM neural networks with time-varying delays on time scales

On a new type of almost periodic time scales, a class of BAM neural networks is considered. By employing a fixed point theorem and differential inequality techniques, some sufficient conditions ensuring the existence and global exponential stability of C¹-almost periodic solutions for this class of networks with time-varying delays are established. Two examples are given to show the effectiveness of the proposed method and results.

Existence and stability of periodic solution of impulsive neural systems with complex deviating arguments

This paper discusses a class of impulsive neural networks with the variable delay and complex deviating arguments. By using Mawhin's continuation theorem of coincidence degree and the Halanay-type inequalities, several sufficient conditions for impulsive neural networks are established for the existence and globally exponential stability of periodic solutions, respectively. Furthermore, the obtained results are applied to some typical impulsive neural network systems as special cases, with a real-life example to show feasibility of our results.

Hopf bifurcation of an (n + 1) -neuron bidirectional associative memory neural network model with delays

Recent studies on Hopf bifurcations of neural networks with delays are confined to simplified neural network models consisting of only two, three, four, five, or six neurons. It is well known that neural networks are complex and large-scale nonlinear dynamical systems, so the dynamics of the delayed neural networks are very rich and complicated. Although discussing the dynamics of networks with a few neurons may help us to understand large-scale networks, there are inevitably some complicated problems that may be overlooked if simplified networks are carried over to large-scale networks. In this paper, a general delayed bidirectional associative memory neural network model with n + 1 neurons is considered. By analyzing the associated characteristic equation, the local stability of the trivial steady state is examined, and then the existence of the Hopf bifurcation at the trivial steady state is established. By applying the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction and stability of the bifurcating periodic solution. Furthermore, the paper highlights situations where the Hopf bifurcations are particularly critical, in the sense that the amplitude and the period of oscillations are very sensitive to errors due to tolerances in the implementation of neuron interconnections. It is shown that the sensitivity is crucially dependent on the delay and also significantly influenced by the feature of the number of neurons. Numerical simulations are carried out to illustrate the main results.