Related papers: Synchronizing distant nodes: a universal classific…
Recently there is a surge of interest in network geometry and topology. Here we show that the spectral dimension plays a fundamental role in establishing a clear relation between the topological and geometrical properties of a network and…
Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However the investigation of their collective phenomena is only at its infancy. Here we…
We present the interplay between synchronization of unidirectional coupled chaotic nodes with heterogeneous delays and the greatest common divisor (GCD) of loops composing the oriented graph. In the weak chaos region and for GCD=1 the…
Many real-world complex systems rely on cluster synchronization to function properly. A cluster of nodes exhibits synchronous behavior while others behave erratically. Predicting the emergence of these clusters and understanding the…
A generalized model of starlike network is suggested that takes into account non-additive coupling and nonlinear transformation of coupling variables. For this model a method of analysis of synchronized cluster stability is developed. Using…
Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization…
In this Rapid Communication we investigate spatially constrained networks that realize optimal synchronization properties. After arguing that spatial constraints can be imposed by limiting the amount of `wire' available to connect nodes…
In this paper, the transition of synchronizing path of delay-coupled chaotic oscillators in a scale-free network is highlighted. Mainly, through the critical transmission delay makes chaotic oscillators be coupled on the edge of stability,…
Existence of different kinds of synchronizations, namely anticipatory, complete and lag type synchronizations (both exact and approximate), are shown to be possible in time-delay coupled piecewise linear systems. We deduce stability…
In these notes we study synchronizability of dynamical processes defined on complex networks as well as its interplay with network topology. Building from a recent work by Barahona and Pecora [Phys. Rev. Lett. 89, 054101 (2002)], we use a…
We present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
We study the stability of the fixed-point solution of an array of mutually coupled logistic maps, focusing on the influence of the delay times, $\tau_{ij}$, of the interaction between the $i$th and $j$th maps. Two of us recently reported…
In this paper, the complete synchronization problem of linearly coupled neural networks with reaction-diffusion terms and time-varying delays via aperiodically intermittent pinning control is investigated. The coupling matrix for the…
We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the instability of each spatial mode (pattern) we…
We study delay-induced transitions in consensus dynamics on signed networks with a ring topology. The proposed model is formulated as a system of delay differential equations incorporating both cooperative and antagonistic interactions, as…
Synchronization of network-coupled dynamical units is important to a variety of natural and engineered processes including circadian rhythms, cardiac function, neural processing, and power grids. Despite this ubiquity, it remains poorly…
Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we…
The field of network synchronization has seen tremendous growth following the introduction of the master stability function (MSF) formalism, which enables the efficient stability analysis of synchronization in large oscillator networks.…
Networks of chaotic units with static couplings can synchronize to a common chaotic trajectory. The effect of dynamic adaptive couplings on the cooperative behavior of chaotic networks is investigated. The couplings adjust to the activities…