Multistability and Stabilization of Fractional-Order Competitive Neural Networks With Unbounded Time-Varying Delays

Saturation function-based continuous control on fixed-time synchronization of competitive neural networks

Currently, through proposing discontinuous control strategies with the signum function and discussing separately short-term memory (STM) and long-term memory (LTM) of competitive artificial neural networks (ANNs), the fixed-time (FXT) synchronization of competitive ANNs has been explored. Note that the method of separate analysis usually leads to complicated theoretical derivation and synchronization conditions, and the signum function inevitably causes the chattering to reduce the performance of the control schemes. To try to solve these challenging problems, the FXT synchronization issue is concerned in this paper for competitive ANNs by establishing a theorem of FXT stability with switching type and developing continuous control schemes based on a kind of saturation functions. Firstly, different from the traditional method of studying separately STM and LTM of competitive ANNs, the models of STM and LTM are compressed into a high-dimensional system so as to reduce the complexity of theoretical analysis. Additionally, as an important theoretical preliminary, a FXT stability theorem with switching differential conditions is established and some high-precision estimates for the convergence time are explicitly presented by means of several special functions. To achieve FXT synchronization of the addressed competitive ANNs, a type of continuous pure power-law control scheme is developed via introducing the saturation function instead of the signum function, and some synchronization criteria are further derived by the established FXT stability theorem. These theoretical results are further illustrated lastly via a numerical example and are applied to image encryption.

Stabilization of reaction-diffusion fractional-order memristive neural networks

This paper investigates the stabilization control of fractional-order memristive neural networks with reaction-diffusion terms. With regard to the reaction-diffusion model, a novel processing method based on Hardy-Poincarè inequality is introduced, as a result, the diffusion terms are estimated associated with the information of the reaction-diffusion coefficients and the regional feature, which may be beneficial to obtain conditions with less conservatism. Then, based on Kakutani's fixed point theorem of set-valued maps, new testable algebraic conclusion for ensuring the existence of the system's equilibrium point is obtained. Subsequently, by means of Lyapunov stability theory, it is concluded that the resulting stabilization error system is global asymptotic/Mittag-Leffler stable with a prescribed controller. Finally, an illustrative example about is provided to show the effectiveness of the established results.

Anti-periodic motion and mean-square exponential convergence of nonlocal discrete-time stochastic competitive lattice neural networks with fuzzy logic

This paper firstly establishes the discrete-time lattice networks for nonlocal stochastic competitive neural networks with reaction diffusions and fuzzy logic by employing a mix techniques of finite difference to space variables and Mittag-Leffler time Euler difference to time variable. The proposed networks consider both the effects of spatial diffusion and fuzzy logic, whereas most of the existing literatures focus only on discrete-time networks without spatial diffusion. Firstly, the existence of a unique ω-anti-periodic in distribution to the networks is addressed by employing Banach contractive mapping principle and the theory of stochastic calculus. Secondly, global exponential convergence in mean-square sense to the networks is discussed on the basis of constant variation formulas for sequences. Finally, an illustrative example is used to show the feasible of the works in the current paper with the help of MATLAB Toolbox. The work in this paper is pioneering in this regard and it has created a certain research foundations for future studies in this area.

Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays

This study on the local stability of quaternion-valued neural networks is of great significance to the application of associative memory and pattern recognition. In the research, we study local Lagrange exponential stability of quaternion-valued neural networks with time delays. By separating the quaternion-valued neural networks into a real part and three imaginary parts, separating the quaternion field into 34n subregions, and using the intermediate value theorem, sufficient conditions are proposed to ensure quaternion-valued neural networks have 34n equilibrium points. According to the Halanay inequality, the conditions for the existence of 24n local Lagrange exponentially stable equilibria of quaternion-valued neural networks are established. The obtained stability results improve and extend the existing ones. Under the same conditions, quaternion-valued neural networks have more stable equilibrium points than complex-valued neural networks and real-valued neural networks. The validity of the theoretical results were verified by an example.