Tradeoff analysis between time cost and energy cost for fixed-time synchronization of discontinuous neural networks.

This article focuses on the tradeoff analysis between time and energy costs for fixed-time synchronization (FXTS) of discontinuous neural networks (DNNs) with time-varying delays and mismatched parameters. First, a more comprehensive lemma is systematically established to study fixed-time stability, which is less conservative than those in most current results. Besides, theoretical proof has proven that the upper bounds of the settling time (ST) in this article are more accurate compared to existing results. Second, on the grounds of the new fixed-time stability lemma, fixed-time synchronization problem for discontinuous neural networks with time-varying delays and mismatched parameters is explored, and sufficient conditions for fixed-time synchronization are obtained. Further, the upper bounds of energy cost during the synchronization process are estimated. Third, in order to achieve a balance between time cost and energy cost, the genetic algorithm is utilized to find the satisfactory control parameter. Finally, a numerical example is provided to verify the theoretical analysis's correctness and the control mechanism's feasibility.

Synchronization in Finite-Time of Delayed Fractional-Order Fully Complex-Valued Dynamical Networks via Non-Separation Method.

The finite-time synchronization (FNTS) problem for a class of delayed fractional-order fully complex-valued dynamic networks (FFCDNs) with internal delay and non-delayed and delayed couplings is studied by directly constructing Lyapunov functions instead of decomposing the original complex-valued networks into two real-valued networks. Firstly, a mixed delay fractional-order mathematical model is established for the first time as fully complex-valued, where the outer coupling matrices of the model are not restricted to be identical, symmetric, or irreducible. Secondly, to overcome the limitation of the use range of a single controller, two delay-dependent controllers are designed based on the complex-valued quadratic norm and the norm composed of its real and imaginary parts' absolute values, respectively, to improve the synchronization control efficiency. Besides, the relationships between the fractional order of the system, the fractional-order power law, and the settling time (ST) are analyzed. Finally, the feasibility and effectiveness of the control method designed in this paper are verified by numerical simulation.

Improved Results on Fixed-/Preassigned-Time Synchronization for Memristive Complex-Valued Neural Networks.

This article concerns the problems of synchronization in a fixed time or prespecified time for memristive complex-valued neural networks (MCVNNs), in which the state variables, activation functions, rates of neuron self-inhibition, neural connection memristive weights, and external inputs are all assumed to be complex-valued. First, the more comprehensive fixed-time stability theorem and more accurate estimations on settling time (ST) are systematically established by using the comparison principle. Second, by introducing different norms of complex numbers instead of decomposing the complex-valued system into real and imaginary parts, we successfully design several simpler discontinuous controllers to acquire much improved fixed-time synchronization (FXTS) results. Third, based on similar mathematical derivations, the preassigned-time synchronization (PATS) conditions are explored by newly developed new control strategies, in which ST can be prespecified and is independent of initial values and any parameters of neural networks and controllers. Finally, numerical simulations are provided to illustrate the effectiveness and superiority of the improved synchronization methodology.

Synchronization of a novel model for memristive neural networks via sliding mode control.

In this paper, a novel memristive neural networks model is developed. In the new model, the states of memristors are related to the initial resistance of the memristors and the amount of charge flowing through them in a specific direction, which embodies the memory characteristic of memristors. As a consequence, parameters in the model vary continuously and cannot be determined by the states of neurons. Existing results on synchronization of memristive neural networks are useless to this model. To investigate the synchronization of the new model, the main difficulty is how to deal with the time-varying parameter mismatches between the drive and response networks. Since the error is unbounded and only utilizing output feedback control is not enough, a sliding mode controller is designed. An integral sliding surface is designed for the desired sliding motion, and a feasible control law is proposed. Moreover, an example is given to demonstrate the novelty of our model and to illustrate the effectiveness of the sliding mode controller.

Exponential synchronization of generalized neural networks with mixed time-varying delays and reaction-diffusion terms via aperiodically intermittent control.

In this paper, the exponential synchronization problem of generalized reaction-diffusion neural networks with mixed time-varying delays is investigated concerning Dirichlet boundary conditions in terms of p-norm. Under the framework of the Lyapunov stability method, stochastic theory, and mathematical analysis, some novel synchronization criteria are derived, and an aperiodically intermittent control strategy is proposed simultaneously. Moreover, the effects of diffusion coefficients, diffusion space, and stochastic perturbations on the synchronization process are explicitly expressed under the obtained conditions. Finally, some numerical simulations are performed to illustrate the feasibility of the proposed control strategy and show different synchronization dynamics under a periodically/aperiodically intermittent control.

Synchronization criteria for generalized reaction-diffusion neural networks via periodically intermittent control.

In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.

Exponential synchronization of stochastic neural networks with leakage delay and reaction-diffusion terms via periodically intermittent control.

We explore the issue of integrating leakage delay, stochastic noise perturbation, and reaction-diffusion effects into the study of synchronization for neural networks with time-varying delays. By using Lyapunov stability theory and stochastic analysis approaches, a periodically intermittent controller is proposed to guarantee the exponential synchronization of proposed coupled neural networks based on p-norm. Some existing results are improved and extended. The usefulness and superiority of our theoretical results are illustrated by a numerical example.

Exponential synchronization of stochastic Cohen-Grossberg neural networks with mixed time-varying delays and reaction-diffusion via periodically intermittent control.

The issue of exponential synchronization for Cohen-Grossberg neural networks with mixed time-varying delays, stochastic noise disturbance and reaction-diffusion effects is investigated. An approach combining Lyapunov stability theory with stochastic analysis approaches and periodically intermittent control is taken to investigate this problem. The proposed criterion for exponential synchronization generalizes and improves those reported recently in the literature. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme.