Response of energy envelop in complex oscillator networks to external stochastic excitations

Abstract

The response of energy envelop in complex nonlinear oscillator networks to stochastic excitations is studied. First, by using the stochastic averaging method for quasi-nonintegrable-Hamiltonian systems, the averaged Fokker–Planck–Kolmogorov equation governing the probability density of the Hamiltonian is established. Then, the stationary probability density of the Hamiltonian is derived, and the stationary probability density of the averaged energy as well as the statistical moments of the Hamiltonian is obtained. To that end, an illustrative example is provided with the analytical relationship between the response and the network parameters as well as the network structure. Specific solutions are presented for five representative topological structures. Throughout extensive simulations, the effects of system parameters, such as the network size, coupling strength and intensities of stochastic excitations on the response of the energy envelop of the networks, are carefully observed and analyzed.