Dynamical Behaviors of Delayed Neural Network Systems with Discontinuous Activation Functions

Authors:
Wenlian Lu;Tianping Chen
Affiliations:
Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai, 200433, People's Republic of China;Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai, 200433, People's Republic of China
Venue:
Neural Computation
Year:
2006

Citing 5
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Abstract

In this letter, without assuming the boundedness of the activation functions, we discuss the dynamics of a class of delayed neural networks with discontinuous activation functions. A relaxed set of sufficient conditions is derived, guaranteeing the existence, uniqueness, and global stability of the equilibrium point. Convergence behaviors for both state and output are discussed. The constraints imposed on the feedback matrix are independent of the delay parameter and can be validated by the linear matrix inequality technique. We also prove that the solution of delayed neural networks with discontinuous activation functions can be regarded as a limit of the solutions of delayed neural networks with high-slope continuous activation functions.