Dynamical model and control of a small-world network with memory

Abstract

This paper proposes a dynamical model of influence volume of small-world-network with memory to investigate the effects of multiple delays on network dynamics. We calculate the influence volume covered by the spreading quantity, discuss the effect of finite size on the network dynamics, and then give the saturate time. The dynamical control is also investigated by introducing the delayed state feedback to simulate the adaptivity of network. With properly chosen delay and gain in feedback path, the controlled model may have stable equilibrium, periodic solution, quasi-periodic solution, or a complex chaotic attractor from a sequence of period-doubling bifurcations. It shows delayed feedback control may find important applications in the management and dynamical control of complex networks.