Related papers: Integrable order parameter dynamics of globally co…
Common noise acting on a population of identical oscillators can synchronize them. We develop a description of this process which is not limited to the states close to synchrony, but provides a global picture of the evolution of the…
We construct nonlinear squeezed states of a generalized isotonic oscillator potential. We demonstrate the non-existence of dual counterpart of nonlinear squeezed states in this system. We investigate statistical properties exhibited by the…
In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to…
We study a generic model of globally coupled rotors that includes the effects of noise, phase shift in the coupling, and distributions of moments of inertia and natural frequencies of oscillation. As particular cases, the setup includes…
In this work, we investigate an important class of nonequilibrium dynamics in the form of nonreciprocal interactions. In particular, we study how nonreciprocal coupling between two $O(n_i)$ order parameters (with $i=1,2$) affects the…
Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Li\'enard type oscillators exhibit this interesting property. We show that a…
This paper is concerned with the dynamics of an infinite-dimensional gradient system under small almost periodic perturbations. Under the assumption that the original autonomous system has a global attractor given as the union of unstable…
We consider an array of nearest-neighbor coupled nonlinear autonomous oscillators with quenched random frequencies and purely conservative coupling. We show that global phase-locked states emerge in finite lattices and study numerically…
We revisit the mean field model of globally and harmonically coupled parametric oscillators subject to periodic block pulses with initially random phases. The phase diagram of regions of collective parametric instability is presented, as is…
Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now…
The superintegrability of a rational harmonic oscillator (non-central harmonic oscillator with rational ratio of frequencies) with non-linear "centrifugal" terms is studied. In the first part, the system is directly studied in the Euclidean…
In this work we formulate a generalized theoretical model to describe the nonlinear dynamics observed in combined frequency-amplitude modulators whose characteristic parameters exhibit a nonlinear dependence on the input modulating signal.…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase dynamics in this system. Our model is a generalization of a…
We show that coexisting domains of coherent and incoherent oscillations can be induced in an ensemble of any identical nonlinear dynamical systems using the nonlocal rotational matrix coupling with an asymmetry parameter. Further, chimera…
This paper considers the oscillations modeled by a forced Van der Pol generalized oscillator. These oscillations are described by a nonlinear differential equation of the form $…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…
The coherent state of a nonlinear oscillator having a nonlinear spectrum is constructed using Gazeau Klauder formalism. The weighting distribution and the Mandel parameter are studied. Details of the revival structure arising from different…
Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…