Related papers: Codimension-two Bifurcations Induce Hysteresis Beh…
We report finite size numerical investigations and mean field analysis of a Kuramoto model with inertia for fully coupled and diluted systems. In particular, we examine for a Gaussian distribution of the frequencies the transition from…
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
In this work, two-cluster modes are studied in a system of globally coupled Kuramoto-Sakaguchi phase oscillators with inertia. It is shown that these regimes can be of two types: with a constant intercluster phase difference rotating at the…
In this work we consider two-dimensional critical manifolds in planar fast-slow systems near fold and so-called canard (=`duck') points. These higher-dimension, and lower-codimension, situation is directly motivated by the case of…
A common external forcing can cause a saddle-node bifurcation in an ensemble of identical Duffing oscillators by breaking the symmetry of the individual bistable (double-well) unit. The strength of the forcing determines the separation…
The Kuramoto model provides a prototypical framework to synchronization phenomena in interacting particle systems. Apart from full phase synchrony where all oscillators behave identically, identical Kuramoto oscillators with ring-like…
We show that su(2) rational and trigonometric Gaudin models, or in other words, generalised coupled angular momenta systems, have singularities that undergo Hamiltonian Hopf bifurcations. In particular, we find a normal form for the…
We consider the Yamada model for an excitable or self-pulsating laser with saturable absorber, and study the effects of delayed optical self-feedback in the excitable case. More specifically, we are concerned with the generation of stable…
In this article, the phenomenon of delayed Hopf bifurcations (DHB) in reaction-diffusion PDEs is analyzed in the cubic Complex Ginzburg-Landau equation with a slowly-varying parameter. We use the classical asymptotic methods of stationary…
We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each others basin volume. This counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed…
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…
We present an unfolding of the codimension-two scenario of the simultaneous occurrence of a discontinuous bifurcation and an Andronov-Hopf bifurcation in a piecewise-smooth, continuous system of autonomous ordinary differential equations in…
Nonlinear normal modes are periodic orbits that survive in nonlinear many-body Hamiltonian systems, and their instability is crucial for relaxation dynamics. Here, we study the instability process of the $\pi/3$-mode in the…
We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution…
Phase-locked states with a constant phase shift between the neighboring oscillators are studied in rings of identical Kuramoto oscillators with time-delayed nearest-neighbor coupling. The linear stability of these states is derived and it…
Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…
In this work we study the local coupled Kuramoto model with periodic boundary conditions. Our main objective is to show how analytical solutions may be obtained from symmetry assumptions, and while we proceed on our endeavor we show apart…
Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean…
We study the emergence of symmetric oscillatory behavior in multi-agent systems where each agent incorporates a continuous memory of its past states and past rates of change, modeled by distributed retarded and neutral delays. The…
We consider a piecewise linear two-dimensional dynamical system that couples a linear equation with the so-called stop operator. Global dynamics and bifurcations of this system are studied depending on two parameters. The system is…