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The effects of a distributed 'weak generic kernel' delay on cyclically coupled limit cycle and chaotic oscillators are considered. For coupled Van der Pol oscillators (and in fact, other oscillators as well) the delay can produce…
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 effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise…
In this expository paper, which covers material presented at the NATO Advanced Study Institute "Nonlinear Analysis, Differential Equations, and Control" (Montreal, Jul/Aug 1998), we deal with several questions related to stability and…
The role of anharmonic effects on the excitation of the double giant dipole resonance is investigated in a simple macroscopic model.Perturbation theory is used to find energies and wave functions of the anharmonic ascillator.The cross…
We study the influence of telegraph noise on synchrony of limit cycle oscillators. Adopting the phase description for these oscillators, we derive the explicit expression for the Lyapunov exponent. We show that either for weak noise or…
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…
Pulse stabilization of cycles with Prediction-Based Control including noise and stochastic stabilization of maps with multiple equilibrium points is analyzed for continuous but, generally, non-smooth maps. Sufficient conditions of global…
The interplay of positive and negative feedback loops on different time scales appears to be a fundamental mechanisms for robust and tunable oscillations in both biological systems and electro-mechanical systems. We develop a detailed…
We consider controller design for robust output tracking and disturbance rejection for continuous-time periodic linear systems with periodic reference and disturbance signals. As our main results we present four different controllers: A…
We investigate synchronization in the presence of delay time modulation for application to communication. We have observed that the robust synchronization is established by a common delay signal and its threshold is presented using Lyapunov…
The synchronized phase of globally coupled nonlinear oscillators subject to noise fluctuations is studied by means of a new analytical approach able to tackle general couplings, nonlinearities, and noise temporal correlations. Our results…
The analysis of a birhythmic modified van der Pol type oscillator driven by periodic excitation and L\`evy noise shows the possible occurrence of coherence resonance and stochastic resonance. The frequency of the harmonic excitation in the…
Conventional weak-coupling Rayleigh-Schr\"odinger perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale analysis, a powerful and sophisticated…
We address the distinction between dynamical and additive noise in time series analysis by making a joint evaluation of both the statistical continuity of the series and the statistical differentiability of the reconstructed measure. Low…
Problem of damping of an arbitrary number of linear oscillators under common bounded control is considered. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the…
Oscillations in nonequilibrium noisy systems are important physical phenomena. These oscillations can happen in autonomous biochemical oscillators such as circadian clocks. They can also manifest as subharmonic oscillations in periodically…
This paper concerns the reliability of a pair of coupled oscillators in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations regardless of the network's initial…
In this paper, an attempt has been made to understand the parametric excitation of a periodic orbit of nonlinear oscillator which can be a limit cycle, center or a slowly decaying center-type oscillation. For this a delay model is…
In the present work, we consider nonlinear control systems for which there exist structural obstacles to the design of classical continuous backstepping feedback laws. We conceive feedback laws such that the origin of the closed-loop system…