Related papers: Analytical Phase Reduction for Weakly Nonlinear Os…
Thomas and Lindner (2014, Phys.Rev.Lett.) defined an asymptotic phase for stochastic oscillators as the angle in the complex plane made by the eigenfunction, having a complex eigenvalue with a least negative real part, of the backward…
In this paper, Van der pol equation has been analyzed for stability and bifurcation phenomena with and without forcing component. Analytical solution of the Van der pol equation using Method of Multiple Scales (MMS) is compared with…
We consider a system of coupled oscillators with finite inertia and time-delayed interaction, and investigate the interplay between inertia and delay both analytically and numerically. The phase velocity of the system is examined; revealed…
In this paper we consider the nonlinear inverse problem of phase retrieval in the context of dynamical sampling. Where phase retrieval deals with the recovery of signals & images from phaseless measurements, dynamical sampling was…
Given the high dimensionality and underlying complexity of many oscillatory dynamical systems, phase reduction is often an imperative first step in control applications where oscillation timing and entrainment are of interest.…
Coupled nonlinear systems under certain conditions exhibit phase synchronization, which may change for different frequency bands or with presence of additive system noise. In both cases, Fourier filtering is traditionally used to preprocess…
We study collective behavior of locally coupled limit-cycle oscillators with random intrinsic frequencies, spatially extended over $d$-dimensional hypercubic lattices. Phase synchronization as well as frequency entrainment are explored…
We study the manifestation of antiphase synchronization in a system of n Rossler Oscillators coupled through a dynamic environment. When the feedback from system to environment is positive (negative) and that from environment to system is…
Phase response curve is an important tool in studies of stable self-sustained oscillations; it describes a phase shift under action of an external perturbation. We consider multistable oscillators with several stable limit cycles. Under a…
Van der Pol and Rayleigh oscillators are two traditional paradigms of nonlinear dynamics. They can be subsumed into a general form of Li\'enard--Levinson--Smith(LLS) system. Based on a recipe for finding out maximum number of limit cycles…
A limit cycle is a self-sustained periodic motion appearing in autonomous ordinary differential equations. As the period of the limit cycle is a-priori unknown, it is challenging to find them as stationary states of a rotating ansatz.…
The equation of the Van der Pol oscillator, being characterized by a dissipative term, is non-Lagrangian. Appending an additional degree of freedom we bring the equation in the frame of action principle and thus introduce a one-way coupled…
The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…
In the present work we examine the dynamics of a model for oscillons in 1-dimensional spacetime field theories with a cubic nonlinearity. We utilize a reduction of the model to first and third harmonics, which leads to a reduced partial…
Weak measurement amplification, which is considered as a very promising scheme in precision measurement, has been applied to various small physical quantities estimation. Since many quantities can be converted to phase signal, it is thus…
Phase reduction is an effective theoretical and numerical tool for studying synchronization of coupled deterministic oscillators. Stochastic oscillators require new definitions of asymptotic phase. The $Q$-function, i.e. the slowest…
Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand…
I have first discussed how averaging theory can be an effective tool in solving weakly non-linear oscillators. Then I have applied this technique for a Van der Pol oscillator and extended the stability criterion of a Van der Pol oscillator…
We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions:…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…