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Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only…
Synchronization is studied in a spatially-distributed network of weekly-coupled, excitatory neurons of Hodgkin-Huxley type. All neurons are coupled to each other synaptically with a fixed time delay and a coupling strength inversely…
We study the generalized synchronization and its stability using master stability function (MSF), in a network of coupled nearly identical dynamical systems. We extend the MSF approach for the case of degenerate eigenvalues of the coupling…
Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection…
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
The emergence of order in nature manifests in different phenomena, with synchronization being one of the most representative examples. Understanding the role played by the interactions between the constituting parts of a complex system in…
Collective behavior plays a key role in the function of a wide range of physical, biological, and neurological systems where empirical evidence has recently uncovered the prevalence of higher-order interactions, i.e., structures that…
Many oscillator networks are multistable, meaning that different synchronization states are realized depending on the initial conditions. In this paper, we numerically analyze a ring network of phase oscillators, in which synchronous states…
We study the existence and stability of synchronous solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. We present a comprehensive stability diagram in the parameter…
We construct a system of $N$ interacting particles on the unit sphere $S^{d-1}$ in $d$-dimensional space, which has $d$-body interactions only. The equations have a gradient formulation derived from a rotationally-invariant potential of a…
Adaptive networks change their connectivity with time, depending on their dynamical state. While synchronization in structurally static networks has been studied extensively, this problem is much more challenging for adaptive networks. In…
In the past few years, the discoveries of small-world and scale-free properties of many natural and artificial complex networks have stimulated significant advances in better understanding the relationship between the topology and the…
The phenomenon of synchronization, where entities exhibit stable oscillations with aligned frequencies and phases, has been detected in diverse areas of natural science. It plays a crucial role in achieving frequency locking in multiple…
Based on recent advances in fibration symmetry theory, we investigate how structural symmetries influence synchronization in systems with higher-order interactions (HOI). Using bipartite graph representations, we identify a node partition…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
We analyze the influence of multiplayer interactions and network adaptation on the stability of equilibrium points in evolutionary games. We consider the Snowdrift game with both two-player and three-player interactions on simplicial…
We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function,…
An outstanding problem in the study of networks of heterogeneous dynamical units concerns the development of rigorous methods to probe the stability of synchronous states when the differences between the units are not small. Here, we…
We give a succinct and self-contained description of the synchronized motion on networks of mutually coupled oscillators. Usually, the stability criterion for the stability of synchronized motion is obtained in terms of Lyapunov exponents.…
We study self-organized (s-) and driven (d-) synchronization in coupled map networks for some simple networks, namely two and three node networks and their natural generalization to globally coupled and complete bipartite networks. We use…