Complete Convergence of Competitive Neural Networks with Different Time Scales

Abstract

This paper studies the complete convergence of a class of neural networks with different time scales under the assumption that the activation functions are unsaturated piecewise linear functions. Under this assumption, there are multiple equilibrium points in the neural network. Traditional methods cannot be used in this neural network. Complete convergence is proved by constructing an energy-like function. Simulations are employed to illustrate the theory.

Some New Stability Properties of Dynamic Neural Networks With Different Time-Scales

“…If the weights of dynamic neural networks (2) are bounded, A, B, C and D in (10) are chosen such that B is non-singular Hurwitz matrix, A − CB −1 D is Hurwitz, Q P , and Q S are selected such that P and S are the solutions of (18), we choose γ > 0 such that inequality (22) is satisfied, then system (2) is asymptotically stable for 0 ≤ ≤ * , where * = min( * 1 , * 2 ), * 1 and * 2 are given in (23).…”

“…The complete convergence of different time-scales neural networks is proved in Ref. 22. The global exponential stability of the delayed competitive neural networks with different time scales is discussed in Ref.…”

Aτ-type stability criteria in division regions for multitime-scale networks with delays

“…It is worth noting that there exist interesting topics about multistability research for muititime‐scale competitive neural networks : The existing ones incorporated global Lipschitz condition into convergent criteria and attained monostability results. Some new multistable dynamics could not be directly revealed by using the existing approaches. Sigmoidal or piecewise linear activation properties are employed in and for multistability analysis of muititime‐scale competitive networks. So, inevitably, some limitations on application for a general class of competitive networks exist. Delay coupled neurons can exhibit complex multistable activation dynamics .…”

Passivity Analysis of Dynamic Neural Networks with Different Time-scales

“…The complete convergence of different time-scales neural networks is proved in Ref. [26]. The global exponential stability of the delayed competitive neural networks with different time scales is discussed in Ref.…”