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Discrete Breathers, which are dynamical localizations of energy observed in the response of periodic, discrete Hamiltonian lattices to external forcing, have been recently observed in the response of micro-scale cantilever arrays. In this article, the authors invoke an analytical formalism introduced in their previous work to study the influence of white noise excitation on the formation and destruction of discrete breathers in a micro-scale cantilever array with strong intersite nonlinearities. The Fokker-Planck equation for a typical element of the array is derived. Numerical solutions to a system of approximate moment evolution equations obtained from the Fokker-Planck equation elucidate the influence of noise of varying intensity on the emergence and sustenance of discrete breathers in the array. The reported results can form the basis for developing a fundamental understanding of the influence of noise on breathers in coupled arrays of nonlinear oscillators with strong intersite nonlinearities including arrays of microelectromechanical systems.

Synchronization behavior is discussed in a clustered neuronal network, in which Rulkov maps with additive noise are applied as building blocks. Additive noise applied here is used to make the Rulkov map generate spiking activities. It is revealed that clustered structure of networks in noisy environments is able to make the subnetwork more synchronous but suppress the synchrony of the entire network meanwhile. The effects of the cluster number, the coupling strength and the noise intensity on spatiotemporal synchronization in the network are discussed. The obtained results are helpful for understanding the clustered structure in cortical systems of the brain from a new viewpoint of synchronization.

The effects of additive Gaussian white noise on neuronal firings of a heterogeneous neuronal network are discussed in this paper. Heterogeneity is introduced through a multiplicative noise term. We show that the mean firing rate and spatiotemporal order of the studied network can attach to a maximum value at some intermediate noise intensities of the additive noise. Furthermore, we find that the optimal noise intensity needed increases with the coupling strength of the neuronal network. And we also give some comparisons with other works.

The effects of the topological probability, the coupling strength and the noise intensity on synchronization of a small-world neuronal network are studied. Chaotic burst synchronization can be bserved as the probability and the coupling strength are large enough. Moreover, the bursting activity and the spatiotemporal patterns are robust to small noise.

A very large number of experimental and theoretical investigations has been devoted to study wave phenomena in the magnetosphere. Many reviews have been written regarding this subject (1–7).

Maps associated to the impact dynamics of simplified one- and two-step gearbox models are derived.