Synchronization transitions are investigated in small-world neuronal networks that are locally modeled by the Rulkov map with additive spatiotemporal noise. In particular, we investigate the impact of different information transmission delays and rewiring probability. We show that short delays induce zigzag fronts of excitations, whereas intermediate delays can further detriment synchrony in th...

Under the existence of system uncertainties and external disturbances, complete synchronization and anti-synchronization between two identical or different hyperchaotic systems are investigated in the paper. Firstly, an active control is used to eliminate the nonlinear part of the error. Then the sliding mode controller is designed based on suitable sliding surface. After that the adaptive upda...

Hybrid synchronization of chaotic systems is a research problem with a goal to synchronize the states of master and slave chaotic systems in a hybrid manner, namely, their even states are completely synchronized (CS) and odd states are anti-synchronized. This paper deals with the research problem of hybrid synchronization of chaotic systems. First, a detailed analysis is made on the qualitative...

In this paper, the global projective synchronization of fractional-order neural networks is investigated. First, a sufficient condition in the sense of Caputo's fractional derivation to ensure the monotonicity of the continuous and differential functions and a new fractional-order differential inequality are derived, which play central roles in the investigation of the fractional adaptive contr...

Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a time delay appears in the interaction which might obstruct synchronization. Here we study the synchronization properties of interconnected networks of oscillato...

Open-plus-closed-loop(OPCL) control method is a more general and physically realizable coupling scheme that can provide stable CS(complete synchronization) and AS(anti-synchronization) in identical and mismatched oscillators. Grosu et. al,[111, 112] recently reported projective synchronization in chaotic systems through open-plus-closed-loop(OPCL) coupling. Hyperchaotic systems possessing at le...