Synchronization For Time-varying Networks Research Articles

Stability analysis of synchronization in long-range temporal networks using theory of dichotomy.

Most of the previous studies on the stability analysis of synchronization in static or time-varying networks are based on the master stability function approach, which is a semi-analytical concept. The necessary and sufficient conditions for synchronization in time-varying networks are challenging problems since the last few years. We focus on the stability analysis of synchronization in time-varying networks, particularly long-range networks. The use of dichotomy theory to derive sufficient conditions for synchronization in this context is an interesting approach. The incorporation of long-range interactions adds complexity and might lead to larger regions of synchronization, providing valuable insights into the dynamics of such networks. Analyzing the co-action of the time-varying nature in the network topology and long-range interactions is a relevant and challenging task, especially when the network is not synchronized. This work appears to explore the interplay between these factors and their impact on synchronization. Additionally, the numerical study considering long-range connections governed by a power-law within the framework of an Erdös-Rényi random network is a practical way to validate and test the analytical results. It is good to see that we are exploring the effects of varying parameters such as rewiring probability, coupling strength, and power-law exponent on the synchronization state.

Mean square [formula omitted] synchronization for time-varying networks with double delays partial differential systems of Markov jump topology

This paper discusses the mean-square exponential synchronization and H∞ synchronization of double time-delays partial differential systems(PDSs) with Markov jump topology. First, based on the Lyapunov functional approach and Dynkins formula, sufficient conditions are obtained for the mean-square synchronization of double time-varying delays PDSs with Markov jump topology and these conditions are presented by linear matrix inequalities (LMIs). Moreover, the mean-square H∞ synchronization of time-delay coupled PDSs with external disturbances is also derived in terms of LMIs, which guarantee the H∞ synchronization of the coupled PDSs with Markov jump topology. Finally, numerical examples of coupled time-delay PDSs are given to illustrate the correctness of the obtained results.

Spatial groups and cyclic oscillations induced by positive correlation between moving direction and phase of mobile oscillators

Lots of studies on synchronization focus on networks with static topologies, but ignore the synchronization in time-varying networks. We study the synchronization of the system in which agents carrying phase oscillators move in two-dimensional lattice with periodic boundary conditions and only interact with their neighbors. In particular, we assume that the direction of movement of an agent is positively correlated to the phase of the oscillator. By numerical simulations, we find cyclic oscillations in the phase transition to synchronization. Remarkably, the oscillators cluster spatially toward the oscillators with higher natural frequency to form groups. And the groups will collapse from the center, as coupling strength exceeds the critical value. In addition, we investigate the effect of moving speed on synchronization and find that the cyclic oscillation during synchronization will disappear with the increment of moving speed.

Synchronization of Sampled-data Coupling Nonlinear Systems in Time-varying Networks

This paper investigates synchronization in time-varying networks of nonlinear systems with sampled-data couplings. In particular, we consider the synchronization problem of systems with a time-varying network structure realized by switching between multiple network structures, including the completely disconnected network. Throughout this paper, we derive a synchronization condition for sampled-data network systems with such a time-varying network structure by introducing a concept of the average dwell time. Finally, we show a numerical simulation result to illustrate the validity of the derived condition.

Interaction between synchronization and motion in a system of mobile agents.

In this paper, we study synchronization in time-varying networks inherited by the Vicsek's model of self-propelled particles. In our model, each particle/agent moves in a two dimensional space according to the Vicsek's rules and is associated to a chaotic system. The dynamics of two oscillators are coupled with each other only when agents are at a distance less than an interaction radius. We investigate the system behavior with respect to some fundamental parameters, and, in particular, to the noise level, which for increasing intensity drives the system from an ordered motion to a disordered one. We show that the global dynamics is ruled by the interplay between motion characteristics and dynamical coupling with synchronization either favored or inhibited by a coordinated motion of the self-propelled particles. Finally, we provide semi-analytical estimation for the synchronization thresholds for interconnections occurring at a time-scale shorter than that of the associated dynamical systems.

Synchronization in time-varying networks.

We study the stability of the synchronized state in time-varying complex networks using the concept of basin stability, which is a nonlocal and nonlinear measure of stability that can be easily applied to high-dimensional systems [P. J. Menck, J. Heitzig, N. Marwan, and J. Kurths, Nature Phys. 9, 89 (2013)]. The time-varying character is included by stochastically rewiring each link with the average frequency f. We find that the time taken to reach synchronization is lowered and the stability range of the synchronized state increases considerably in dynamic networks. Further we uncover that small-world networks are much more sensitive to link changes than random ones, with the time-varying character of the network having a significant effect at much lower rewiring frequencies. At very high rewiring frequencies, random networks perform better than small-world networks and the synchronized state is stable over a much wider window of coupling strengths. Lastly we show that the stability range of the synchronized state may be quite different for small and large perturbations, and so the linear stability analysis and the basin stability criterion provide complementary indicators of stability.

Synchronization in time-varying networks: A matrix measure approach

Synchronization in complex networks has attracted lots of interest in various fields. We consider synchronization in time-varying networks, in which the weights of links are time varying. We propose a useful approach--i.e., the matrix measure approach--to derive some analytically sufficient conditions for synchronization in time-varying networks. These conditions are less conservative than many existing synchronization conditions. Theoretical analysis and numerical simulations of different networks verify our main results.