A New Approach for Estimating the Attraction Domain for Hopfield-Type Neural Networks

Abstract

In this letter, using methods proposed by E. Kaslik, St. Balint, and their colleagues, we develop a new method, expansion approach, for estimating the attraction domain of asymptotically stable equilibrium points of Hopfield-type neural networks. We prove theoretically and demonstrate numerically that the proposed approach is feasible and efficient. The numerical results that obtained in the application examples, including the network system considered by E. Kaslik, L. Brăescu, and St. Balint, indicate that the proposed approach is able to achieve better attraction domain estimation.

Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks

“…In this article, we have designed the new model of Hopfield type neural networks with unpredictable perturbations and derive sufficient conditions of the existence, uniqueness, and asymptotic stability of the strongly unpredictable oscillations, which develop previously known results in [3][4][5][6][7][8][9][10], and others.…”

“…In the last decades, many works have been devoted to the study of Hopfield type neural networks. For example, periodic and almost periodic solutions [3,4], exponential stability [5][6][7], domain of attraction and convergence rate [8][9][10] have been deeply investigated.…”

Enlarging the domain of attraction and maximising convergence rate for delta operator systems with actuator saturation

“…Although these problems have been examined extensively from various aspects recently, estimating and enlarging the domain of attraction is still a difficult task which remains unsolved up to now [16], [17]. Although many methods have been developed to determine an inner approximation of the domain of attraction, please refer to [18], [19], [20], [21] and the references therein. The particular control of delta operator systems with actuator saturation was not proved before.…”

Approximation on attraction domain of Cohen–Grossberg neural networks

“…Under the assumption of diagonalizability of Jacobian matrix at the equilibrium point, the optimal Lyapunov function method was proposed by Kaslik and Balint [8], which provides a way in approximating the attraction domain. In 2009, an iterative expansion approach for improving the approximation of attraction domain was presented [9]. Employing this iterative expansion approach, a better approximation of the attraction domain is achieved.…”