Stability analysis of fractional Quaternion-Valued Leaky Integrator Echo State Neural Networks with multiple time-varying delays

Abstract

This paper studies the stability problem of fractional order continuous-time Quaternion-Valued Leaky Integrator Echo State Neural Networks (NN) with multiple time-varying delays. The NN is decomposed into four real-valued systems without considering the non-commutativity of quaternion multiplication resulting in Hamilton rules. Then, the delay-independent stability analysis of the NN equilibrium point with Lipschitz continuous activation function is derived in the real space. The existence and uniqueness of the equilibrium point are also given using the contraction map in the real space. Simulations results show the feasibility of the method.