Related papers: Suppressing birhythmicity by parametrically modula…
We introduce a scalar reduction method for forced or coupled systems with nonlinearities in both heterogeneity and coupling strength. Heterogeneity is formulated as a relatively weak but nonlinear alteration of the vector field(s). The…
Classical self-sustained oscillators, that generate periodic motion without periodic external forcing, are ubiquitous in science and technology. The realization of nonclassical self-oscillators is an important goal of quantum physics. We…
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…
Phase reduction is a dimensionality reduction scheme to describe the dynamics of nonlinear oscillators with a single phase variable. While it is crucial in synchronization analysis of coupled oscillators, analytical results are limited to…
We consider rare transitions induced by colored noise excitation in multistable systems. We show that undesirable transitions can be mitigated by a simple time-delay feedback control if the control parameters are judiciously chosen. We…
Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is…
The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…
We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a…
We study the stabilization of networked control systems with asynchronous sensors and controllers. Offsets between the sensor and controller clocks are unknown and modeled as parametric uncertainty. First we consider multi-input linear…
This paper considers the oscillations modeled by a forced Van der Pol generalized oscillator. These oscillations are described by a nonlinear differential equation of the form $…
Phase control of parametric modulation in coupled oscillator networks enables sculpting of dynamical states with desired spatiotemporal symmetries. Symmetry-aware Floquet analysis successfully predicts such states in linear systems, but…
We show that quantum-interference phenomena can be realized for the dissipative nonlinear systems exhibiting hysteresis-cycle behavior and quantum chaos. Such results are obtained for a driven dissipative nonlinear oscillator with…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
Synchronization is a major concept in nonlinear physics. In a large number of systems, it is observed at long times for a sinusoidal excitation. In this paper, we design a transiently non-sinusoidal driving to reach the synchronization…
We use an extension of the van der Pol oscillator as an example of a system with multiple time scales to study the susceptibility of its trajectory to polynomial perturbations in the dynamics. A striking feature of many nonlinear,…
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…
In the absence of external forcing, all trajectories on the phase plane of the van der Pol oscillator tend to a closed, periodic, trajectory -- the limit cycle -- after infinite time. Here, we drive the van der Pol oscillator with an…
Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the…
Synchronization forms the basis of many coordination phenomena in natural systems, enabling them to function cohesively and support their fundamental operations. However, there are scenarios where synchronization disrupts a system's proper…
Pyragas time delayed feedback control has proven itself as an effective tool to non-invasively stabilize periodic solutions. In a number of publications, this method was adapted to equivariant settings and applied to stabilize branches of…