Related papers: Oscillations in Mixed-Feedback Systems
The objective of the present study is to mitigate, or even completely eliminate, the limit cycle oscillations in mechanical systems using a passive nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA). An unconventional…
We develop a predictor-feedback control design for multi-input nonlinear systems with distinct input delays, of arbitrary length, in each individual input channel. Due to the fact that different input signals reach the plant at different…
We show that the equivalent linearization technique, when used properly, enables us to calculate frequency corrections of weakly nonlinear oscillators beyond the first order in nonlinearity. We illustrate the method by applying it to the…
Birhythmicity arises in several physical, biological and chemical systems. Although, many control schemes are proposed for various forms of multistability, only a few exist for controlling birhythmicity. In this paper we investigate the…
In this paper, we apply the averaging method via Brouwer degree in a class of planar systems given by a linear center perturbed by a sum of continuous homogeneous vector fields, to study lower bounds for their number of limit cycles. Our…
A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…
In this paper we are concerned with determining lower bounds of the number of limit cycles for piecewise polynomial holomorphic systems with a straight line of discontinuity. We approach this problem with different points of view: study of…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
Oscillator networks found in social and biological systems are characterized by the presence of wide ranges of coupling strengths and complex organization. Yet robustness and synchronization of oscillations are found to emerge on…
The orbits of the reversible differential system $\dot{x}=-y$, $\dot{y}=x$, $\dot{z}=0$, with $x,y \in R$ and $z\in R^d$, are periodic with the exception of the equilibrium points $(0,0, z)$. We compute the maximum number of limit cycles…
We present a method to determine the relative parameter mismatch in a collection of nearly identical chaotic oscillators by measuring large deviations from the synchronized state. We demonstrate our method with an ensemble of slightly…
Considering Limit Cycles as one of the limits of Lienard equation, an analyis analogous to centre manifold analysis has been done for a $3-D$ nonlinear system exhibiting Limit Cycle. A rigorous study on radius of the Limit Cycle orbit has…
In this Letter, we derive a sufficient condition of synchronizing limit sets (attractors and repellers) by using the linear feedback control technique proposed here. There examples are included. The numerical simulations and computer…
We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated to the probability density of oscillators with a given…
We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit…
In this paper some aspects on the periodic solutions of the extended Duffing-Van der Pol oscillator are discussed. Doing different rescaling of the variables and parameters of the system associated to the extended Duffing-Van der Pol…
The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed…
Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees…
In this work, we address the problem of identifying sparse continuous-time dynamical systems when the spacing between successive samples (the sampling period) is not constant over time. The proposed approach combines the…
We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.