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An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…

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…

The Kuramoto model is a canonical framework for analyzing phase synchronization, yet its utility is restricted to the vicinity of the oscillator's unperturbed limit cycle. Here, we present a method to construct coupled-oscillator models…

We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is…

We solve a longstanding stability problem for the Kuramoto model of coupled oscillators. This system has attracted mathematical attention, in part because of its applications in fields ranging from neuroscience to condensed-matter physics,…

For a general time-varying system, we prove that existence of an "Output Robust Control Lyapunov Function" implies existence of continuous time-varying feedback stabilizer, which guarantees output asymptotic stability with respect to the…

By means of numerical integration we investigate the coherent and incoherent phases in a generalized Kuramoto model of phase-coupled oscillators with distance-dependent delay. Preserving the topology of a complete graph, we arrange the…

We consider piecewise linear discrete time macroeconomic models, which possess a continuum of equilibrium states. These systems are obtained by replacing rational inflation expectations with a boundedly rational, and genuinely sticky,…

This paper gives sufficient conditions for having complete synchronization of oscillators in connected undirected networks. The considered oscillators are not necessarily identical and the synchronization terms can be nonlinear. An…

We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…

Experimental realization and quantitative investigation of common-noise-induced synchronization of limit-cycle oscillations subject to random telegraph signals are performed using an electronic oscillator circuit. Based on our previous…

Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…

We study global-in-time behavior of the solution to a reaction-diffusion system with mass conservation, as proposed in the study of cell polarity, particularly, the second model of \cite{oi07}. First, we show global-in-time existence of…

We propose a network of oscillators to retrieve given patterns in which the oscillators keep a fixed phase relationship with one another. In this description, the phase and the amplitude of the oscillators can be regarded as the timing and…

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…

An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…

The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling. The population is described by a Fokker-Planck equation…

We consider discontinuous dynamics of integrate-and-fire models, which consist of pulse-coupled biological oscillators. A thoroughly constructed map is in the basis of the analysis. Synchronization of non-identical oscillators is…

We propose a general Langevin equation describing the universal properties of synchronization transitions in extended systems. By means of theoretical arguments and numerical simulations we show that the proposed equation exhibits,…

We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…