Systems of nonlinear differential equations with periodic coefficients, which include Hill's and Mathieu's equations as examples in the linear limit, are important from a practical point of view. Nonlinear Hill's equations model a variety of dynamical systems of interest to physics and...

This paper studies the dynamics of a network-based SIS epidemic model with nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological effect of certain diseases spread in a contact network at high infective levels. We first find a threshold value for...

We study the dependence of synchronization transitions in small-world networks of bursting neurons with hybrid electrical–chemical synapses on the information transmission delay, the probability of electrical synapses, and the rewiring probability. It is shown that, irrespective of the...

The auto-correlation function and the cross-correlation function of an autonomous stochastic system with time delays are investigated. We obtain the distribution curves of the auto-correlation function Cx(s) and Cy(s), and the cross-correlation function Cxy(s) and Cyx(s) of the stochastic...

Feedback flashing ratchets are thermal rectifiers that use information on the state of the system to operate the switching on and off of a periodic potential. They can induce directed transport even with symmetric potentials thanks to the asymmetry of the feedback protocol. We investigate here...

Time delays commonly exist in the real world. In the present work we consider weighted general complex dynamical networks with time delay, which are undirected and connected. Control of such networks, by applying local feedback injections to a fraction of network nodes, is investigated for both...

The steady state response and bifurcation of nonlinear random business cycle model to random narrow-band excitation with time delay state feedback are studied in this paper. The method of multiple scales is used to determine the business cycle model of modulation of amplitude and phase. The...

Here some ideas related with delayed unstable systems are exposed. In particular, two simple dynamics where antagonistic forces, one of them being a time-delayed and randomly modulated force, are presented as prototypes to study the apparency of a critical balance that is seen as a transient...

In this paper, we investigate synchronization in oscillator networks with small-world (SW) interactions and coupling delays. We derive a stability criterion for the network synchronized state. We show that the stability of the synchronized state is independent of the network topology, that is,...