Related papers: Short chaotic strings and their behaviour in the s…
We study the dynamics of a nonlinear one-dimensional disordered system from a spectral point of view. The spectral entropy and the Lyapunov exponent are extracted from the short time dynamics, and shown to give a pertinent characterization…
A model for a lattice of coupled cat maps has been recently introduced. This new and specific choice of the coupling makes the description especially easy and nontrivial quantities as Lyapunov exponents determined exactly. We studied the…
We show that two initially weakly coupled chaotic systems can achieve self-organized synchronization by adaptively reducing their speed and/or enhancing the coupling strength. Explicit adaptive algorithms for speed-reduction and…
We show that the dynamical behavior of a coupled map lattice where the individual maps are Bernoulli shift maps can be solved analytically for integer couplings. We calculate the invariant density of the system and show that it displays a…
We present a new coupling scheme to control spatio-temporal patterns and chimeras on 1-d and 2-d lattices and random networks of discrete dynamical systems. The scheme involves coupling with an external lattice or network of damped systems.…
We present explicit examples of semi-realistic heterotic models with spontaneously broken supersymmetry, which dynamically lead to breaking scales much smaller than $M_{\rm Planck}$ and exponentially small positive values for the…
We analyze nonlocally coupled networks of identical chaotic oscillators with either time-discrete or time-continuous dynamics (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent…
A one-dimensional chain of sporadic maps with asymmetric nearest neighbour couplings is numerically studied. It is shown that in the region of strong asymmetry the system becomes spatially fully synchronized, even in the thermodinamic…
This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived.…
Collective oscillations of lattices of locally-coupled chaotic Roessler oscillators are studied with regard to the dynamical scaling of their phase interfaces. Using analogies with the complex Ginzburg-Landau and the Kardar-Parisi-Zhang…
We develop a formalism for the quantization of topologically stable excitations in the 4-dimensional abelian lattice gauge theory. The excitations are global and local (Abrikosov-Nielsen-Olesen) strings and monopoles. The operators of…
We consider the singularly perturbed limit of periodically excited two-dimensional FitzHugh-Nagumo systems. We show that the dynamics of such systems are essentially governed by an one-dimensional map and present a numerical scheme to…
Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits ($T$) of a dynamical system scales as a…
The Nikolaevskiy model for pattern formation with continuous symmetry exhibits spatiotemporal chaos with strong scale separation. Extensive numerical investigations of the chaotic attractor reveal unexpected scaling behavior of the…
At early stages the dynamics of cosmic string networks is expected to be influenced by an excessive production of small loops at the scales of initial conditions l_{min}. To understand the late time behavior we propose a very simple…
In the realm of spatiotemporal chaos, unstable periodic orbits play a major role in understanding the dynamics. Their stability changes and bifurcations in general are thus of central interest. Here, coupled map lattice discretizations of…
The bifurcation and chaotic behaviour of unidirectionally coupled deterministic ratchets is studied as a function of the driving force amplitude ($a$) and frequency ($\omega$). A classification of the various types of bifurcations likely to…
We investigate coupled circle maps in presence of feedback and explore various dynamical phases observed in this system of coupled high dimensional maps. We observe an interesting transition from localized chaos to spatiotemporal chaos. We…
Applying chaos theory for secure digital communications is promising and it is well acknowledged that in such applications the underlying chaotic systems should be carefully chosen. However, the requirements imposed on the chaotic systems…
The characteristic stretching and squeezing of chaotic motion is linearized within the finite number of phase space domains which subdivide a classical baker map. Tensor products of such maps are also chaotic, but a more interesting…