相关论文: Coherence versus reliability of stochastic oscilla…
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,…
Laser resonances play a crucial role in optical and quantum systems because the photons impact the stability and coherence of laser sources. While laser oscillations are typically stable and periodic, the presence of nonlinear effects can…
Intracellular transmission of information via chemical and transcriptional networks is thwarted by a physical limitation: the finite copy number of the constituent chemical species introduces unavoidable intrinsic noise. Here we provide a…
We investigate the effects of dichotomous noise added to a classical harmonic oscillator in the form of stochastic time-dependent gain and loss states, whose durations are sampled from two distinct exponential waiting time distributions.…
For the paradigmatic case of the damped quantum harmonic oscillator we present two measurement-based feedback schemes to control the stability of its fixed point. The first scheme feeds back a Pyragas-like time-delayed reference signal and…
A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators…
Much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state---provided the dependence is known. In this paper we consider the delay…
Reproducibility of a noisy limit-cycle oscillator driven by a random piecewise constant signal is analyzed. By reducing the model to random phase maps, it is shown that the reproducibility of the limit cycle generally improves when the…
We study the reliability of large networks of coupled neural oscillators in response to fluctuating stimuli. Reliability means that a stimulus elicits essentially identical responses upon repeated presentations. We view the problem on two…
We propose a method for detecting the presence of synchronization of self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of self-sustained…
Collective electron transport causes a weakly coupled semiconductor superlattice under dc voltage bias to be an excitable system with $2N+2$ degrees of freedom: electron densities and fields at $N$ superlattice periods plus the total…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
Robotic control systems are increasingly relying on distributed feedback controllers to tackle complex sensing and decision problems such as those found in highly articulated human-centered robots. These demands come at the cost of a…
Self-sustained oscillators are ubiquitous and essential for metrology, communications, time reference, and geolocation. In its most basic form an oscillator consists of a resonator driven on-resonance, through feedback, to create a periodic…
We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…
The Van der Pol equation is a paradigmatic model of relaxation oscillations. This remarkable nonlinear phenomenon of self-sustained oscillatory motion underlies important rhythmic processes in nature and electrical engineering. Relaxation…
We study the cooling performance of optical-feedback controllers for open optical and mechanical resonators in the Linear Quadratic Gaussian setting of stochastic control theory. We utilize analysis and numerical optimization of closed-loop…
Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous…