Related papers: First-order route to antiphase clustering in adapt…
We study the efficiency of synchronization in ensembles of identical coupled stochastic oscillator systems. By deriving a chemical Langevin equation, we measure the rate at which the systems synchronize. The rate at which the difference in…
We investigate the transition to synchronization in adaptive multilayer networks with higher-order interactions both analytically and numerically in the presence of phase frustration ($\beta$). The higher order topology consists of pairwise…
Experiments and supporting theoretical analysis is presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation,…
Collective behavior in large ensembles of dynamical units with non-pairwise interactions may play an important role in several systems ranging from brain function to social networks. Despite recent work pointing to simplicial structure,…
Using recent dimensionality reduction techniques in large systems of coupled phase oscillators exhibiting bistability, we analyze complex macroscopic behavior arising when the coupling between oscillators is allowed to evolve slowly as a…
Neural networks are commonly trained to make predictions through learning algorithms. Contrastive Hebbian learning, which is a powerful rule inspired by gradient backpropagation, is based on Hebb's rule and the contrastive divergence…
Synchronization in a population of oscillators with hyperbolic chaotic phases is studied for two models. One is based on the Kuramoto dynamics of the phase oscillators and on the Bernoulli map applied to these phases. This system possesses…
We investigate the impact of contrarians (via negative coupling) in a multilayer network of phase oscillators having higher-order interactions. We show that the multilayer framework facilitates synchronization onset in the negative pairwise…
Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…
We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the…
Dynamical systems on networks with adaptive couplings appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. We investigate a paradigmatic system of adaptively coupled phase…
Adaptation plays a fundamental role in shaping the structure of a complex network and improving its functional fitting. Even when increasing the level of synchronization in a biological system is considered as the main driving force for…
In this letter, we present an elegant method to build and maintain an anti-phase configuration of two nonlinear oscillators with different natural frequencies and dynamics described by the sinusoidal phase-reduced model. The anti-phase…
We introduce an interaction mechanism between oscillators leading to exact anti-phase and in-phase synchronization. This mechanism is applied to the coupling between two nonlinear oscillators with a limit cycle in phase space, leading to a…
In-phase synchronization is a special case of synchronous behavior when coupled oscillators have the same phases for any time moments. Such behavior appears naturally for nearly identical coupled limit-cycle oscillators when the coupling…
We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…
In a quasi-1D thermal convective system consisting of a large array of nonlinearly coupled oscillators, clustering is the way to achieve a regime of mostly antiphase synchronized oscillators. This regime is characterized by a spatiotemporal…
We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions:…
Synchronization has received a lot of attention from the scientific community for systems evolving on static networks or higher-order structures, such as hypergraphs and simplicial complexes. In many relevant real world applications, the…
We develop a linear response theory by computing the asymptotic value of the order parameter from the linearized equation of continuity around the nonsynchronized reference state using the Laplace transform in time. The proposed theory is…