Search

In this paper, some complex phenomena of dynamical bifurcations are shown for a two-neural network with delay coupling. The sigmoid activation function with slope ratio, a monotonically increasing function, is proposed to consider the relations of the sigmoid and Hardlim functions. The equilibrium points are studied analytically in detail in terms of the characteristic equation and static bifurcation. The central manifold reduction and normal form method are employed to determine Hopf bifurcation and its stability. The stable equilibrium points and periodic motions are observed in different parameter regions. Effects of slope ratio and delayed coupling on dynamic behaviors are investigated by the numerical simulation, such as Poincare map, phase portraits, and power spectrum. Various active transitions to chaos and the corresponding critical boundaries on the focused parameter regions are obtained to classify dynamical behaviors including stable equilibrium point, periodic solution, 2-torus, 3-torus, and then the chaotic motions. [ABSTRACT FROM AUTHOR]