Related papers: Oscillations in Mixed-Feedback Systems
We propose a convex optimization procedure for black-box identification of nonlinear state-space models for systems that exhibit stable limit cycles (unforced periodic solutions). It extends the "robust identification error" framework in…
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of…
In the context of studying periodic processes, this paper investigates first under which conditions switching affine systems in the plane generate stable limit cycles. Based on these conditions, a design methodology is proposed by which the…
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…
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,…
Recently, several studies have investigated synchronization in quantum-mechanical limit-cycle oscillators. However, the quantum nature of these systems remained partially hidden, since the dynamics of the oscillator's phase was overdamped…
In this paper, we introduce novel equations that are dual to the ones of the well-known invariant ellipsoids method. These equations yield ellipsoids with newly established geometrical interpretations and connections to linear system norms.…
Canard cycles are periodic orbits that appear as special solutions of fast-slow systems (or singularly perturbed Ordinary Differential Equations). It is well known that canard cycles are difficult to detect, hard to reproduce numerically,…
Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the…
The paper revisits recently revealed regimes of the "nonconventional synchronization" in systems of coupled bi-stable Van der Pol oscillators. These regimes are characterized by periodic (or quasiperiodic) almost complete energy exchanges…
In recent papers we have introduced a method for the study of limit cycles of the Lienard system: dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. The method gives a sequence of polynomials R_n(x), whose roots are related to the…
Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are…
Nonlinear oscillators are commonly encountered in a wide range of physical and engineering systems, exhibiting rich and complex dynamics. Among these, the Van der Pol oscillator is well known for its self-sustained limit cycle behavior.…
We report a transition from homogeneous steady state to inhomogeneous steady state in coupled oscillators, both limit cycle and chaotic, under cyclic coupling and diffusive coupling as well when an asymmetry is introduced in terms of a…
This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…
Iteration limited model predictive control (MPC) can stabilize a feedback control system under sufficient conditions; this work explores combining a low iteration limit MPC with a high iteration limit MPC for mixed-integer quadratic…
We provide an upper bound for the number of limit cycles that planar polynomial differential systems of a given degree may have. The bound turns out to be a polynomial of degree four in the degree of the system. The strategy brings together…
We study the implementation of a weak multiple delayed feedback for controlling coherence of chaotic oscillations. The specific system we treat is the Lorenz system with classical set of parameters. There are two reasons behind the interest…
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…
Model Predictive Control (MPC) is often tuned by trial and error. When a baseline linear controller exists that is already well tuned in the absence of constraints and MPC is introduced to enforce them, one would like to avoid altering the…