Related papers: A laminar chaotic saddle within a turbulent attrac…
We show that, in periodically perturbed chaotic systems, Phase Synchronization appears, associated to a special type of stroboscopic map, in which not only averages quantities are equal to invariants of the perturbation, the angular…
The transition from complex-periodic to chaotic behavior is investigated in oscillatory media supporting spiral waves. We find turbulent regimes characterized by the spontaneous nucleation, proliferation and erratic motion of…
External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a…
The Superconducting QUantum Interference Device (SQUID) is a highly nonlinear oscillator with rich dynamical behavior, including chaos. When driven by a time-periodic magnetic flux, the SQUID exhibits extreme multistability at frequencies…
Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…
The asymptotic travelling wave solution of the KdV-Burgers equation driven by the long scale periodic driver is constructed. The solution represents a shock-train in which the quasi-periodic sequence of dispersive shocks or soliton chains…
The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even…
The multiple time scale dynamics induced by radiation pressure and photothermal effects in a high-finesse optomechanical resonator is experimentally studied. At difference with two-dimensional slow-fast systems, the transition from the…
Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as…
One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are…
We present a mechanism for the emergence of strange attractors (observable chaos) in a two-parameter periodically-perturbed family of differential equations on the plane. The two parameters are independent and act on different ways in the…
This paper analyses the Hamiltonian model of drift waves which describes the chaotic transport of particles in the plasma confinement. With one drift wave the system is integrable and it presents stable orbits. When one wave is added the…
Although synchronization has been extensively studied, important processes underlying its emergence have remained hidden by the use of global order parameters. Here, we uncover how the route unfolds through a sequential transition between…
The recent discovery of unstable travelling waves (TWs) in pipe flow has been hailed as a significant breakthrough with the hope that they populate the turbulent attractor. We confirm the existence of coherent states with internal fast and…
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…
An aspect of the synchronization dynamics is investigated in this work. We argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits unstable dimension variability. Unstable dimension…
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which \textit{unstable…
The dynamics of unidirectionally coupled chaotic Lorenz systems is investigated. It is revealed that chaos is present in the response system regardless of generalized synchronization. The presence of sensitivity is theoretically proved, and…
Conflict between formation of a cyclonic vortex and isotropization in forced homogeneous rotating turbulence is numerically investigated. It is well known that a large rotation rate of the system induces columnar vortices to result in…
The flow past inline oscillating rectangular cylinders is studied numerically at a Reynolds number representative of two-dimensional flow. A symmetric mode, known as S-II, consisting of a pair of oppositely-signed vortices on each side,…