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Multistability of Switched Neural Networks With Piecewise Linear Activation Functions Under State-Dependent Switching | IEEE Journals & Magazine | IEEE Xplore

Multistability of Switched Neural Networks With Piecewise Linear Activation Functions Under State-Dependent Switching


Abstract:

This paper is concerned with the multistability of switched neural networks with piecewise linear activation functions under state-dependent switching. Under some reasona...Show More

Abstract:

This paper is concerned with the multistability of switched neural networks with piecewise linear activation functions under state-dependent switching. Under some reasonable assumptions on the switching threshold and activation functions, by using the state-space decomposition method, contraction mapping theorem, and strictly diagonally dominant matrix theory, we can characterize the number of equilibria as well as analyze the stability/instability of the equilibria. More interesting, we can find that the switching threshold plays an important role for stable equilibria in the unsaturation regions of activation functions, and the number of stable equilibria of an n-neuron switched neural network with state-dependent parameters increases to 3n from 2n in the conventional one. Furthermore, for two-neuron switched neural networks, the precise attraction basin of each stable equilibrium point can be figured out, and its boundary is composed of the stable manifolds of unstable equilibrium points and the switching lines. Two simulation examples are discussed in detail to substantiate the effectiveness of the theoretical analysis.
Page(s): 2052 - 2066
Date of Publication: 12 November 2018

ISSN Information:

PubMed ID: 30418927

Funding Agency:


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