Sufficient conditions are obtained for the existence and global exponential stability of a unique equilibrium of a class of two-layer heteroassociative networks called bidirectional associative memory (BAM) networks with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time. An illustrative example is given to demonstrate the effectiveness of the obtained results.

Global exponential stability of BAM neural networks with delays and impulses

New comparison results for impulsive integro-differential equations and applications

Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays

In this paper, the impulsive Cohen–Grossberg neural network model with time-varying delays is considered. Applying the idea of vector Lyapunov function, M-matrix theory and inequality technique, several new sufficient conditions are obtained to ensure global exponential stability of equilibrium point for impulsive Cohen–Grossberg neural network with time-varying delays. These results generalize a few previous known results and remove some restrictions on the neural network. An example is given to show the effectiveness of the obtained results. It is believed that these results are significant and useful for the design and applications of the Cohen–Grossberg neural network.

Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays

This paper illustrates that there is a globally exponentially stable unique equilibrium state in an artificial neural network that is subject to delays distributed over unbounded intervals, and also to large impulses that are not too frequent. The activation functions, which may be unbounded, nondifferentiable and/or nonmonotonic, are assumed to be globally Lipschitz continuous. The stability analysis exploits the method of Lyapunov functions and the technique of Halanay inequalities to derive a family of easily verifiable sufficient conditions for convergence to the unique equilibrium state. The sufficiency conditions, in the norm either ∥ · ∥ p where p ⩾ 1 or ∥ · ∥ ∞ , include those that govern the network parameters and the impulse magnitude and frequency.

Exponential stability of artificial neural networks with distributed delays and large impulses

Global exponential stability and existence of periodic solution of Hopfield-type neural networks with impulses

In this paper, we present large deviation theory that characterizes the exponential estimate for rare events of stochastic dynamical systems in the limit of weak noise. We aim to consider next-to-leading-order approximation for more accurate calculation of mean exit time via computing large deviation prefactors with the research efforts of machine learning. More specifically, we design a neural network framework to compute quasipotential, most probable paths and prefactors based on the orthogonal decomposition of vector field. We corroborate the higher effectiveness and accuracy of our algorithm with a practical example. Numerical experiments demonstrate its powerful function in exploring internal mechanism of rare events triggered by weak random fluctuations.

Computing large deviation prefactors of stochastic dynamical systems based on machine learning


 Massive data from observations, experiments and simulations of dynamical models in scientific and engineering fields make it desirable for data-driven methods to extract basic laws of these models. We present a novel method to identify such high dimensional stochastic dynamical systems that perturbed by a non-Gaussian $\alpha$-stable Lévy noise. More explicitly, firstly a machine learning framework to solve the sparse regression problem is established to grasp the drift terms through one of non-local Kramers-Moyal formulas. Then the jump measure and intensity of the noise are disposed by the relationship with statistical characteristics of the process. Three examples are then given to demonstrate the feasibility. This approach proposes an effective way to understand the complex phenomena of systems under non-Gaussian fluctuations and illuminates some insights into the exploration for further typical dynamical indicators such as the maximum likelihood trasition path or mean exit time of these stochastic systems.

Linghong Lu

Papers

Global exponential stability and existence of periodic solution of Hopfield-type neural networks with impulses

Computing large deviation prefactors of stochastic dynamical systems based on machine learning

Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussian $\alpha$-stable Lévy noise