This paper investigates the dynamic properties of artificial neural networks using differential equations and explores the influence of parameters on stability and neural oscillations. By analyzing the equilibrium point of the differential equations, we identify conditions for asymptotic stability and criteria for oscillation in artificial neural networks. Furthermore, we demonstrate how adjusting synaptic weights between neurons can effectively control stability and oscillation. The proposed model offers potential insights into the malfunctioning mechanisms of biological neural networks implicated in neurological disorders like Parkinson's disease tremors and epilepsy seizures, which are characterized by abnormal oscillations.

PurposeThe purpose of this paper is to study the dynamic behavior of complex-valued switched grey neural network models (SGNMs) with distributed delays when the system parameters and external input are grey numbers.Design/methodology/approachFirstly, by using the properties of grey matrix, M-matrix theory and Homeomorphic mapping, the existence and uniqueness of equilibrium point of the SGNMs were discussed. Secondly, by constructing a proper Lyapunov functional and using the average dwell time approach and inequality technique, the robust exponential stability of the SGNMs under restricted switching was studied. Finally, a numerical example is given to verify the effectiveness of the proposed results.FindingsSufficient conditions for the existence and uniqueness of equilibrium point of the SGNMs have been established; sufficient conditions for guaranteeing the robust stability of the SGNMs under restricted switching have been obtained.Originality/value(1) Different from asymptotic stability, the exponential stability of SGNMs which include grey parameters and distributed time delays will be investigated in this paper, and the exponential convergence rate of the SGNMs can also be obtained; (2) the activation functions, self-feedback coefficients and interconnected matrices are with different forms in different subnetworks; and (3) the results obtained by LMIs approach are complicated, while the proposed sufficient conditions are straightforward, which are conducive to practical applications.