Related papers: First-order route to antiphase clustering in adapt…
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…
In this work, we investigate the implications of the differential Hebbian learning rule known as Input-Correlations (ICO) learning in the classification of synchronization in coupled nonlinear oscillator systems. We are investigating the…
We analyze the simplest model of identical coupled phase oscillators subject to two-body and three-body interactions with permutation symmetry. This model is derived from an ensemble of weakly coupled nonlinear oscillators by phase…
Hebbian and anti-Hebbian plasticity are widely observed in the biological brain, yet their theoretical understanding remains limited. In this work, we find that when a learning method is regularized with L2 weight decay, its learning signal…
Recent studies of dynamic properties in complex systems point out the profound impact of hidden geometry features known as simplicial complexes, which enable geometrically conditioned many-body interactions. Studies of collective behaviours…
Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in…
Synchronization systems with effective inertia, such as power grid networks and coupled electromechanical oscillators, are commonly modeled by the second-order Kuramoto model. In the forward process, numerical simulations exhibit a…
We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit many important collective dynamical states found in other synchronizing systems. The state of our system is specified by a set of…
Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the…
We study the collective dynamics of identical phase oscillators on globally coupled networks whose interactions are asymmetric and mediated by positive and negative couplings. We split the set of oscillators into two interconnected…
We construct an analytical theory of interplay between synchronizing effects by common noise and by global coupling for a general class of smooth limit-cycle oscillators. Both the cases of attractive and repulsive coupling are considered.…
This paper considers the cluster synchronization problem of generic linear dynamical systems whose system models are distinct in different clusters. These nonidentical linear models render control design and coupling conditions highly…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
We present a model of systems of cells with intracellular oscillators (`clocks'). This is motivated by examples from developmental biology and from the behavior of organisms on the threshold to multicellularity. Cells undergo random motion…
In this work we analyze the solutions of a simple system of coupled phase oscillators in which the connectivity is learned dynamically. The model is inspired in the process of learning of birdsong by oscine birds. An oscillator acts as the…
A sufficiently connected topology linking the constituent units of a complex system is usually seen as a prerequisite for the emergence of collective phenomena such as synchronization. We present a random network of heterogeneous phase…
A coupled-phase oscillator model where each oscillator has an angular velocity that varies due to the interaction with other oscillators is studied. This model is proposed to deepen the understanding of the relationship between the…
We propose a coupled system of fast and slow phase oscillators. We observe two-step transitions to quasi-periodic motions by direct numerical simulations of this coupled oscillator system. A low-dimensional equation for order parameters is…
A pair of coupled erbium doped fiber ring lasers is used to explore the dynamics of coupled spatiotemporal systems. The lasers are mutually coupled with a coupling delay less than the cavity round-trip time. We study synchronization between…
Real-world networks are often characterized by simultaneous interactions between multiple agents that adapt themselves due to feedback from the environment. In this article, we investigate the dynamics of an adaptive multilayer network of…