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In this letter, we provide a detailed numerical examination of the dynamics of a charged Thomas oscillator in an external magnetic field. We do so by adopting and then modifying the cyclically symmetric Thomas oscillator to study the…
Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and…
Many natural, living and engineered systems display oscillations that are characterized by multiple timescales. Typically, such systems are described as slow-fast systems, where the slow dynamics result from a hyperbolic slow manifold that…
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…
Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…
We report the synchronization behavior in a one-dimensional chain of identical limit cycle oscillators coupled to a mass-spring load via a force relation. We consider the effect of periodic parametric modulation on the final synchronization…
In this paper non-linear dynamics of a periodically forced excitable glow discharge plasma has been studied. The experiments were performed in glow discharge plasma where excitability was achieved for suitable discharge voltage and gas…
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 noise induced switching in systems far from equilibrium by using an underdamped micromechanical torsional oscillator driven into the nonlinear regime. Within a certain range of driving frequencies, the oscillator possesses two…
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,…
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…
Systems with the coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. In order to describe genetic regulatory networks several…
We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. This…
Synchronization of quantum nonlinear oscillators has attracted much attention recently. To characterize the quantum oscillatory dynamics, we recently proposed a fully quantum-mechanical definition of the asymptotic phase, which is a key…
An all-optically driven strategy to govern a liquid crystalline collective molecular nonlinear oscillator is discussed. It does not require external feedbacks of any kind while the oscillator and a time-depending perturbation both are…
We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are \textit{unstable}. These unstable attractors occur in networks of pulse-coupled oscillators where they prevail for…
We study the nonlinear behaviors of mass-spring systems damped by dry friction using simulation by a nonlinear LC circuit damped by anti-parallel diodes. We show that the differential equation for the electric oscillator is equivalent to…
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…
Many physical, chemical and biological processes rely on intrinsic oscillations to employ resonance responses to external stimuli of certain frequency. Such resonance phenomena in biological systems are typically explained by one of two…
Synchronisation and stability under periodic oscillatory driving are well-understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly…