Multiple stability and instability of Cohen–Grossberg neural network with unbounded time-varying delays

Abstract

Abstract In this paper, multiple stability and instability of Cohen–Grossberg neural network with unbounded time-varying delays are studied. Based on the geometrical configuration of activation functions and some rigorous mathematical analysis, some algebraic criteria are proposed to guarantee coexistence of multiple stable equilibrium points and multiple unstable equilibrium points in the model. Moreover, using the partition space method, we prove that the discussed model has at least 3n $3^{n}$ equilibrium points, 2n $2^{n}$ of them are locally μ-stable and others are unstable. Finally, the numerical example and its simulation show the effectiveness of the proposed results.

Keywords

• Cohen–Grossberg neural network
• Multiple stability and instability
• Unbounded time-varying delays