Nonlinear dynamics of the small-world networks–-Hopf bifurcation, sequence of period-doubling bifurcations and chaos

From viewpoint of nonlinear dynamics, the complex nonlinear dynamic phenomena of the small-world networks are studied in some details. The small-world network model, a set of evolution equations with time delay, is used to approach the nonlinear dynamics of networks, and the stability and Hopf bifurcation of the equilibrium state are investigated numerically in the vector field, and the intermittency phenomena in the networks are explained based on the analysis of Hopf bifurcation. Additionally, the ensuing period-doubling bifurcation, sequence of period-doubling bifurcation and period-3 are studied, and the existence of chaos is verified numerically.