混沌动力学
This work presents numerical evidences that for discrete dynamical systems with one positive Lyapunov exponent the decay of the distance autocorrelation is always related to the Lyapunov exponent. Distinct decay laws for the distance…
Statistical equilibration of energies in a slow-fast system is a fundamental open problem in physics. In a recent paper, it was shown that the equilibration rate in a springy billiard can remain strictly positive in the limit of vanishing…
We study a 2-dimensional model for an antidot periodic superlattice with perturbed positions of the antidots. To do so we use a quasiperiodic LG model obtained from a 3-dimensional billiard model. Our results show that infinite drifting…
We investigate the effect of memory on a chaotic system experimentally and theoretically. For this purpose, we use Chua's oscillator as an electrical model system showing chaotic dynamics extended by a memory element in form of a…
Cluster synchronization is a phenomenon in which oscillators in a given network are partitioned into synchronous clusters. As recently shown, diverse cluster synchronization patterns can be found using network symmetry when the oscillators…
Various features of the development of individual living species, including individual humans, are programmed. Is death also programmed, and if yes, how is it implemented and what can be the underlying mechanism providing the inevitability…
Chaotic Hamiltonians are known to follow Random Matrix Theory (RMT) ensembles in the apparent randomness of their spectra and wavefunction statistics. Deviations form RMT also do occur, however, due to system-specific properties, or as…
In the framework of photogravitational version of the restricted five-body problem, the existence and stability of the in-plane equilibrium points, the possible regions for motion are explored and analysed numerically, under the combined…
This work uses the statistical properties of Finite-Time Lyapunov Exponents (FTLEs) to investigate the Intermittent Stickiness Synchronization (ISS) observed in the mixed phase space of high-dimensional Hamiltonian systems. Full Stickiness…
The Hopf oscillator has been shown to capture many phenomena of the auditory and vestibular systems. These systems exhibit remarkable temporal resolution and sensitivity to weak signals, as they are able to detect sounds that induce motion…
In this paper we continue our studies of the two dimensional caldera potential energy surface in a parametrized family that allows for a study of the effect of symmetry on the phase space structures that govern how trajectories enter,…
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the…
We investigate the geometrical structure of instabilities in the two-scales Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of the full spectrum of covariant Lyapunov vectors reveals the presence of a slow bundle…
The sensitivity of long-time averages of a hyperbolic chaotic system to parameter perturbations can be determined using the shadowing direction, the uniformly-bounded-in-time solution of the sensitivity equations. Although its existence is…
We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the…
We consider a periodically-forced 1-D Langevin equation that possesses two stable periodic solutions in the absence of noise. We ask the question: is there a most likely noise-induced transition path between these periodic solutions that…
Localized states of Harper's equation correspond to strange nonchaotic attractors (SNAs) in the related Harper mapping. In parameter space, these fractal attractors with nonpositive Lyapunov exponents occur in fractally organized…
The synchronization between two dynamical systems is one of the most appealing phenomena occurring in Nature. Already observed by Huygens in the case of two pendula, it is a current area of research in the case of chaotic systems, with…
Noise-induced statistical periodicity in a class of one-dimensional maps is studied. We show the existence of statistical periodicity in a modified Lasota-Mackey map and describe the phenomenon in terms of almost cyclic sets. A transition…
When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of…