Related papers: Extracting phase coupling functions between collec…
Demographic oscillators are individual-based systems exhibiting temporal cycles sustained by the stochastic dynamics of the microscopic interacting particles. We here use the example of coupled predator-prey oscillators to show that…
Optimization of mutual synchronization between a pair of limit-cycle oscillators with weak symmetric coupling is considered in the framework of the phase reduction theory. By generalizing a previous study on the optimization of…
Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…
Controlling rhythmic systems, typically modeled as limit-cycle oscillators, is an important subject in real-world problems. Phase reduction theory, which simplifies the multidimensional oscillator state under weak input to a single phase…
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,…
Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable…
Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems. However, these formulations usually…
Building oscillator based computing systems with emerging nano-device technologies has become a promising solution for unconventional computing tasks like computer vision and pattern recognition. However, simulation and analysis of these…
The paper presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to…
A large variety of rhythms are observed in nature. Rhythms such as electroencephalogram signals in the brain can often be regarded as interacting. In this study, we investigate the dynamical properties of rhythmic systems in two populations…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
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…
Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the…
In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic…
The synchronization behavior of networked chaotic oscillators with periodic coupling is investigated. It is observed in simulations that the network synchronizability could be significantly influenced by tuning the coupling frequency, even…
We study the dynamics of phase synchronization in growing populations of discrete phase oscillatory systems when the division process is coupled to the distribution of oscillator phases. Using mean field theory, linear stability analysis,…
We present a novel method of reconstructing the phase-amplitude dynamics directly from measured electrophysiological signals to estimate the coupling between brain regions. For this purpose, we use the recent advances in the field of…
Collective synchronization is often summarized by a complex order parameter $R e^{i\Psi}$, implicitly treating the global phase $\Psi$ as a meaningful macroscopic coordinate. Here we ask when $\Psi$ becomes \emph{operationally well-defined}…
An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be…
In this paper, we numerically study the stochastic and the deterministic occasional uncoupling methods of effecting identical synchronized states in low dimensional, dissipative, diffusively coupled, chaotic flows that are otherwise not…