混沌动力学
We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. Firstly we introduce a fixed time lag for the elements of each partition that is selected using techniques from…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…
For a globally coupled network of semiconductor lasers with delayed optical feedback, we demonstrate the existence of chimera states. The domains of coherence and incoherence that are typical for chimera states are found to exist for the…
Finding equilibria of the finite size Kuramoto model amounts to solving a nonlinear system of equations, which is an important yet challenging problem. We translate this into an algebraic geometry problem and use numerical methods to find…
We investigate numerically the dynamics of two-dimensional Euler and ideal magnetohydrodynamics (MHD) flows in systems with a finite number of modes, up to $4096^2$, for which several quadratic invariants are preserved by the truncation and…
In this work we study the possibility of detecting the so-called strong stochasticity threshold, i.e. the transition between weak and strong chaos as the energy density of the system is increased, in anharmonic oscillator chains by means of…
We investigate higher-order geometric $k$-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in longitudinal studies of Computational Anatomy. Our…
We propose a novel method of reconstructing the topology and interaction functions for a general oscillator network. An ensemble of initial phases and the corresponding instantaneous frequencies is constructed by repeating random…
For chaotic cavities with scattering leads attached, transport properties can be approximated in terms of the classical trajectories which enter and exit the system. With a semiclassical treatment involving fine correlations between such…
We explore the non-equilibrium escape dynamics of long-range interacting ions in one-dimensional traps. The phase space of the few ion setup and its impact on the escape properties are studied. As a main result we show that an instantaneous…
We present and experimentally demonstrate a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying. At each…
We report the first experimental demonstration of chaotic phase synchronization (CPS) in unidirectionally coupled time-delay systems using electronic circuits. We have also implemented experimentally an efficient methodology for…
We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is…
We consider an application of a general theory for cavities with point-like perturbations for a rectangular shape. Hereby we concentrate on experimental wave patterns obtained for nearly degenerate states. The nodal lines in these patterns…
The entrainment transition of coupled random frequency oscillators presents a long-standing problem in nonlinear physics. The onset of entrainment in populations of large but finite size exhibits strong sensitivity to fluctuations in the…
Systems of coupled oscillators have been seen to exhibit chimera states, i.e. states where the system splits into two groups where one group is phase locked and the other is phase randomized. In this work, we report the existence of chimera…
For the steady-state direct cascade of two-dimensional Navier-Stokes turbulence, we derive analytically the probability of strong vorticity fluctuations. The probability density function (pdf) of the vorticity coarse-grained over a scale in…
Whenever a distinct state is immersed in a sea of complicated and dense states, the strength of the distinct state, which we refer to as a doorway, is distributed in their neighboring states. We analyze this mechanism for 2-D billiards with…
We extend a recent synchronization analysis of exact finite-state sources to nonexact sources for which synchronization occurs only asymptotically. Although the proof methods are quite different, the primary results remain the same. We find…