相关论文: Periodic oscillators, isochronous centers and reso…
Synchronization by exchange of pulses is a widespread phenomenon, observed in flashing fireflies, applauding audiences and the neuronal network of the brain. Hitherto the focus has been on integrate-and-fire oscillators. Here we consider…
This paper addresses the amplitude and phase dynamics of a large system non-linear coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the…
The dynamics of an oscillator driven by both low- and high- frequency external signals is studied. It is shown that both two- and three-frequency resonances arise due to a nonlinear interaction of these harmonic forces. Conditions which…
The phenomenon of superoscillation, where band limited signals can oscillate over some time period with a frequency higher than the band limit, is not only very interesting but it also seems to offer many practical applications. The first…
We propose a simple procedure to identify the collective coordinate $Q$ which is used to generate the isochronous Hamiltonian. The new isochronous Hamiltonian generates more and more isochronous oscillators, recursively.
We consider the phenomenon of mutual synchronization in a fundamental quantum system of two detuned quantum harmonic oscillators dissipating into the environment. We identify the conditions leading to this spontaneous phenomenon showing…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
In the classical (non-quantum) relativity theory the course of the moving clock is dilated as compared to the course of the clock at rest (the Einstein dilation). Any unstable system may be regarded as a clock. The time evolution (e.g., the…
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…
We experimentally demonstrate group synchrony in a network of four nonlinear optoelectronic oscillators with time-delayed coupling. We divide the nodes into two groups of two each, by giving each group different parameters and by enabling…
The 'nice' $x:\mathbf{R}\rightarrow\{0,1\}^{n}$ functions from the asynchronous systems theory are called signals. The periodicity of a point of the orbit of the signal x is defined and we give a note on the existence of the prime period.
Isochronous islands are regular solutions related to different chains of elliptic points but with the same winding number. These isochronous islands emerge in phase space as a response to multiple resonant perturbations and can be simulated…
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…
The amplitude-dependent frequency of the oscillations, termed \emph{nonisochronicity}, is one of the essential characteristics of nonlinear oscillators. In this paper, the dynamics of the Rossler oscillator in the presence of…
The resonant dynamics of a charged particle, governed by the Lorentz force equation in an electromagnetic field generated by a current-carrying wire with a small harmonic modulation, is considered in this study. When regarded as a…
We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators…
We study the dynamical behavior of an ensemble of oscillators interacting through short range bidirectional pulses. The geometry is 1D with periodic boundary conditions. Our interest is twofold. To explore the conditions required to reach…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
In this note we unify the results of A.C. Lazer and P.O. Frederickson [3], A.C. Lazer [6], A.C. Lazer and D.E. Leach [7], J.M. Alonso and R. Ortega [1], and P. Korman and Y. Li [4] on periodic oscillations and unbounded solutions of…