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We study the occurrence of frequency synchronised states with tunable emergent frequencies in a network of connected systems. This is achieved by the interplay between time scales of nonlinear dynamical systems connected to form a network,…
A general scheme for construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the…
Weakly coupled limit cycle oscillators can be reduced into a system of weakly coupled phase models. These phase models are helpful to analyze the synchronization phenomena. For example, a phase model of two oscillators has a one-dimensional…
We consider networks of weakly pulse-coupled identical oscillators. In an effort to resolve a long-standing problem, we develop an analytic condition on the infinitesimal phase response curve (iPRC) for synchronized dynamic behaviour,…
We present an analytical description for the collective dynamics of oscillator ensembles with higher-order coupling encoded by simplicial structure, which serves as an illustrative and insightful paradigm for brain function and information…
The collective behavior of the ensembles of coupled nonlinear oscillator is one of the most interesting and important problems in modern nonlinear dynamics. In this paper, we study rotational dynamics, in particular space-time structures,…
We show that a ring of phase oscillators coupled with transmission delays can be used as a pattern recognition system. The introduced model encodes patterns as stable periodic orbits. We present a detailed analysis of the underlying…
A density oscillator is a fluid system in which oscillatory flow occurs between different density fluids through the pore connecting them. We investigate the synchronization in coupled density oscillators using two-dimensional hydrodynamic…
Gravitational-wave memory is characterized by a signal component that persists after a transient signal has decayed. Treating such signals in the frequency domain is non-trivial, since discrete Fourier transforms assume periodic signals on…
Recent research on the dynamics of certain fluid dynamical instabilities shows that when there is a slow invariant manifold subject to fast timescale instability the dynamics are extremely sensitive to noise. The behaviour of such systems…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture.…
We study stochastic perturbations of ODE with stable limit cycles -- referred to as stochastic oscillators -- and investigate the response of the asymptotic (in time) frequency of oscillations to changing noise amplitude. Unlike previous…
Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order…
There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…
A system's response to external periodic changes can provide crucial information about its dynamical properties. We investigate the synchronization transition, an archetypical example of a dynamic phase transition, in the framework of such…
This study investigates the synchronization dynamics of coupled-oscillator systems in which some of the oscillators are damaged and lose their autonomous oscillations. The damaged elements are modeled using damped oscillators; thus, the…
The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…
We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…