Related papers: Chaotic Explosions
We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an…
We consider spatiotemporal chaotic systems for which spatial correlation functions decay substantially over a length scale xi (the spatial correlation length) that is small compared to the system size L. Numerical simulations suggest that…
We put forward a conjecture of recurrence for a gas of hard spheres that collide elastically in a finite volume. The dynamics consists of a sequence of instantaneous binary collisions. We study how the numbers of collisions of different…
We report experimental evidence of the route to spatiotemporal chaos in a large 1D-array of hotspots in a thermoconvective system. Increasing the driving force, a stationary cellular pattern becomes unstable towards a mixed pattern of…
In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents…
It has been proposed to make practical use of chaos in communication, in enhancing mixing in chemical processes and in spreading the spectrum of switch-mode power suppies to avoid electromagnetic interference. It is however known that for…
The stationary distribution of a fully chaotic system typically exhibits a fractal structure, which dramatically changes if the dynamical equations are even slightly modified. Perturbative techniques are not expected to work in this…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
The spatiotemporal dynamics of an excitable medium with multiple spiral defects is shown to vary smoothly with system size from short-lived transients for small systems to extensive chaos for large systems. A comparison of the Lyapunov…
We propose a strange-attractor model of tumor growth and metastasis. It is a 4-dimensional spatio-temporal cancer model with strong nonlinear couplings. Even the same type of tumor is different in every patient both in size and appearance,…
Dissipationless N-body models of rotating galaxies, iso-energetic to a non-rotating model, are examined as regards the mass in regular and in chaotic motion. The values of their spin parameters $\lambda$ are near the value $\lambda=0.22$ of…
We study a model inspired by the pinball machine involving chaotic scattering of particles on hard disks with inelasticity. This system exhibits sensitivity not only on the initial conditions of the scattering point particle but also on the…
Unstable periodic orbits scar wave functions in chaotic systems. This also influences the associated spectra, that follow the otherwise universal Porter--Thomas intensity distribution. We show here how this deviation extend to other longer…
A new type of perturbative expansion is built in order to give a rigorous derivation and to clarify the range of validity of some commonly used model equations. This model describes the evolution of the modulation of two short and localized…
An area-preserving map of the unit sphere, consisting of alternating twists and turns, is mostly chaotic. A Liouville density on that sphere is specified by means of its expansion into spherical harmonics. That expansion initially…
Departing from classical concepts of ergodic theory, formulated in terms of probability densities, measures describing the chaotic behavior and the loss of information in quantum open systems are proposed. As application we discuss the…
We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with $\mathcal{PT}$ symmetry. For the quantum dynamics, both the mean momentum and mean square of momentum exhibits the staircase…
We adapt ideas from geometrical optics and classical billiard dynamics to consider particle trajectories with constant velocity on a cone with specular reflections off an elliptical boundary formed by the intersection with a tilted plane,…
The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An…
A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is…