Related papers: Higher Dimensional Limit Cycles and Coupling Induc…
Following the paper of K. Shimizu et al. (2011) we consider the Bonhoeffer-van der Pol oscillator with non-autonomous periodic perturbation. We show that the presence of mixed mode oscillations reported in that paper can be explained using…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
In this paper we present an influence of discontinuous coupling on the dynamics of multistable systems. Our model consists of two periodically forced oscillators that can interact via soft impacts. The controlling parameters are the…
The limit cycle of the van der Pol oscillator, $\ddot{x}+ \epsilon (x^2-1) \dot{x} + x =0$, is studied in the plane $(x,\dot{x})$ by applying the homotopy analysis method. A recursive set of formulas that approximate the amplitude and form…
In this article, we investigate the dynamical robustness in a network of relaxation oscillators. In particular, we consider a network of diffusively coupled Van der Pol oscillators to explore the aging transition phenomena. Our…
Synchronization occurs ubiquitously in nature. The van der Pol oscillator has been a favorite model to investigate synchronization. Here we study the oscillator in the deep quantum regime, where nonclassical effects dominate the dynamics.…
We study populations of oscillators, all-to-all coupled by means of quenched disordered phase shifts. While there is no traditional synchronization transition with a nonvanishing Kuramoto order parameter, the system demonstrates a specific…
Effects of synchronization in a system of two coupled oscillators with time-delayed feedback are investigated. Phase space of a system with time delay is infinite-dimensional. Thus, the picture of synchronization in such systems acquires…
The interference between spin-density-wave and superconducting instabilities in quasi-one-dimensional correlated metals is analyzed using the renormalization group method. At the one-loop level, we show how the interference leads to a…
Periodically-driven systems are ubiquitous in science and technology. In quantum dynamics, even a small number of periodically-driven spins leads to complicated dynamics. Hence, it is of interest to understand what constraints such dynamics…
We study the dynamics of the entanglement between two oscillators that are initially prepared in a general two-mode Gaussian state and evolve while coupled to the same environment. In a previous paper we showed that there are three…
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,…
Coupled distinct arrays of nonlinear oscillators have been shown to have a regime of high frequency, or ultra-harmonic, oscillations that are at multiples of the natural frequency of individual oscillators. The coupled array architectures…
This note addresses the output synchronization problem of incrementally output-feedback passive nonlinear systems in the presence of exogenous disturbances. Two kinds of distributed controllers are proposed; one placed at the nodes and the…
Chemical oscillation is an interesting nonlinear dynamical phenomenon which arises due to complex stability condition of the steady state of a reaction far away from equilibrium which is usually characterised by a periodic attractor or a…
In this paper, I aim to study free oscillations of a system of oscillators in more than one dimensions in the absence of damping. The basic approach lies in decoupling the motion in the individual perpendicular directions. Once the…
We study the onset of synchronization in lattices of limit cycle oscillators with long-range coupling by means of numerical simulations. In this regime the critical coupling strength depends on the system size and interaction range…
The simplest ring oscillator is made from three strongly nonlinear elements repressing each other unidirectionally resulting in the emergence of a limit cycle. A popular implementation of this scheme uses repressive genes in bacteria…
We report an interesting symmetry-breaking transition in coupled identical oscillators, namely the continuous transition from homogeneous to inhomogeneous limit cycle oscillations. The observed transition is the oscillatory analog of the…
We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics…