A general approach to multistability analysis for fuzzy multidimensional-valued NNs with memristor.

Abstract

This article addresses a general approach to the multistability analysis for fuzzy multidimensional-valued memristive neural networks(FMVMNNs) with unbounded time-varying delays. By integrating fuzzy logic with memristive dynamics, establishing a generalized analytical approach encompassing real, complex, and quaternion systems. Through general analysis, via state-space decomposition based on the Brouwer fixed point theorem, several sufficient criteria are obtained to ensure the existence of ∏_M=R,I^J,K∏_i=1ⁿ(2S_i^M+1) equilibrium points(EPs), among which ∏_M=R,I^J,K∏_i=1ⁿ(S_i^M+1) are shown to be locally asymptotically stable, where S_i^M are nonnegative integers and the set M depends on the number field. These criteria are less restrictive and easier to verify. This paper further estimate the basins of attraction corresponding to stable equilibria. Finally, the theoretical results are supported by two simulated numerical examples.