Related papers: Global dynamics of oscillator populations under co…
The features of animal population dynamics, for instance, flocking and migration, are often synchronized for survival under large-scale climate change or perceived threats. These coherent phenomena have been explained using synchronization…
The behavior of two unidirectionally coupled chaotic oscillators near the generalized synchronization onset has been considered. The character of the boundaries of the generalized synchronization regime has been explained by means of the…
We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of…
We develop a framework for the general interpretation of the stochastic dynamical system near a limit cycle. Such quasi-periodic dynamics are commonly found in a variety of nonequilibrium systems, including the spontaneous oscillations of…
Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional…
We propose a nonlinear voter model to study the emergence of global consensus in opinion dynamics. In our model, agent $i$ agrees with one of binary opinions with the probability that is a power function of the number of agents holding this…
We investigate global phase coherence in a system of coupled oscillators on a small-world networks constructed from a ring with nearest-neighbor edges. The effects of both thermal noise and quenched randomness on phase ordering are examined…
Robust online estimation of oscillation frequency belongs to classical problems of system identification and adaptive control. The given harmonic signal can be noisy and with varying amplitude at the same time, as in the case of damped…
In this paper, we investigate synchronization of coupled second-order linear harmonic oscillators with random noises and time delays. The interaction topology is modeled by a weighted directed graph and the weights are perturbed by white…
Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. If multiple such networks are coupled together, the question arises whether these rhythms will synchronize. We investigate the impact of…
We study the impact of noise on a neural population rate model of up and down states. Up and down states are typically observed in neuronal networks as a slow oscillation, where the population switches between high and low firing rates…
We analyze populations of Kuramoto oscillators with a particular distribution of natural frequencies. Inspired by networks where there are two groups of nodes with opposite behaviors, as for instance in power-grids where energy is either…
Research on synchronization of coupled oscillators has helped explain how uniform behavior emerges in populations of non-uniform systems. But explaining how uniform populations engage in sustainable non-uniform synchronization may prove to…
Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the…
The spectrum of the evolution Operator associated with a nonlinear stochastic flow with additive noise is evaluated by diagonalization in a polynomial basis. The method works for arbitrary noise strength. In the weak noise limit we…
We analyze an intermediate collective regime where amplitude oscillators distribute themselves along a closed, smooth, time-dependent curve $\mathcal{C}$, thereby maintaining the typical ordering of (identical) phase oscillators. This is…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
The classical motion of a one-dimensional chain of atoms coupled through a specific force function that depends on position shows features very similar to the Wannier-Stark problem of a quantum particle under the combined effects of a…
We explore the interplay of network structure, topology, and dynamic interactions between nodes using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state,…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…