Related papers: Optimal synchronisation to a limit cycle
We investigate how to minimize the work dissipated during nonequilibrium processes. To this end, we employ methods from linear response theory to describe slowly varying processes, i.e., processes operating within the linear regime around…
We analyze the control of the motion of a charged particle by means of an external electric field. The system is constrained to move along a given direction. The goal of the control is to change the speed of the particle in a fixed time…
We show that a wide class of uncoupled limit cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study the stability of the noise-driven…
We show that the equivalent linearization technique, when used properly, enables us to calculate frequency corrections of weakly nonlinear oscillators beyond the first order in nonlinearity. We illustrate the method by applying it to the…
Systems of oscillators subject to time-dependent noise typically achieve synchronization for long times when their mutual coupling is sufficiently strong. The dynamical process whereby synchronization is reached can be thought of as a…
Synchronization is essential for the operation of AC power systems: All generators in the power grid must rotate with fixed relative phases to enable a steady flow of electric power. Understanding the conditions for and the limitations of…
In this paper, we consider the traditional Van der Pol Oscillator with a forcing dependent on a delay in feedback. The delay is taken to be a nonlinear function of both position and velocity which gives rise to many different types of…
We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which…
This paper studies contraction theory with the aim of exploring complete synchronization phenomenon in complex networks of coupled oscillators. We examine the conditions for complete synchronization in three network topologies: all-to-all,…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
We derive a concise and general expression of the energy dissipation rate for coupled oscillators rotating on circular trajectories by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. In the…
We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…
A rationale is provided for the emergence of synchronization in a system of coupled oscillators in a stick-slip motion. The single oscillator has a limit cycle in a region of the state space for each parameter set beyond the supercritical…
For noisy self-sustained oscillators, both reliability, stability of a response to a noisy driving, and coherence understood in the sense of constancy of oscillation frequency belong to the main characteristics. Though the both…
A model of coupled molecular oscillators is proposed to study nonequilibrium thermodynamics of synchronization. We find that synchronization of nonequilibrium oscillators costs energy even when the oscillator-oscillator coupling is…
The chaotic synchronization regime in coupled dynamical systems is considered. It has been shown, that the onset of synchronous regime is based on the appearance of the phase relation between interacting chaotic oscillators frequency…
We study the behaviour of the van der Pol oscillator when either its damping parameter $\mu$ or its nonlinearity parameter $\xi$ is subject to additive or multiplicative random noise. Assuming various power law exponents for the relation…
We study a system of interacting self-propelled particles whose walking velocity depends on the stage of the locomotion cycle. The model introduces a phase equation in the optimal velocity model for vehicular traffic. We find that the…
We present an existence and localization result for periodic solutions of second-order non-linear coupled planar systems, without requiring periodicity for the non-linearities. The arguments for the existence tool are based on a variation…
Different models of self-excited oscillators which are four-dimensional extensions of the van der Pol system are reported. Their symmetries are analyzed. Three of them were introduced to model the release of vortices behind circular…