Related papers: ERROR PROPAGATION IN EXTENDED CHAOTIC SYSTEMS
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
Infinitesimal and finite amplitude error propagation in spatially extended systems are numerically and theoretically investigated. The information transport in these systems can be characterized in terms of the propagation velocity of…
Propagation of initially localized perturbations is investigated in chaotic coupled map lattices with long-range couplings decaying as a power of the distance. The initial perturbation propagates exponentially fast along the lattice, with a…
The scaling behavior of the maximal Lyapunov exponent in chaotic systems with time-delayed feedback is investigated. For large delay times it has been shown that the delay-dependence of the exponent allows a distinction between strong and…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
The dynamics of the system is investigated when one part of the system initially behaves in a regular manner and the other in a chaotic one. The propagation of the chaos is considered as the motion of a region with the maximal Lyapunov…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
We analyze the consequences of iterative measurement-induced nonlinearity on the dynamical behavior of qubits. We present a one-qubit scheme where the equation governing the time evolution is a complex-valued nonlinear map with one complex…
We consider a mechanism for area preserving Hamiltonian systems which leads to the enhanced probability, $P(\lambda, t)$, to find small values of the finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic dynamical…
The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…
Based on the principle of chaotification for continuous-time autonomous systems, which relies on two basic properties of chaos, i.e., globally bounded with necessary positive-zero-negative Lyapunov exponents, this paper derives a feasible…
It is frequently asserted that in a chaotic system two initially close points will separate at an exponential rate governed by the largest global Lyapunov exponent. Local Lyapunov exponents, however, are more directly relevant to…
A kinetic approach is adopted to describe the exponential growth of a small deviation of the initial phase space point, measured by the largest Lyapunov exponent, for a dilute system of hard disks, both in equilibrium and in a uniform shear…
We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a…
We use Lyapunov-like functions and convex optimization to propagate uncertainty in the initial condition of nonlinear systems governed by ordinary differential equations. We consider the full nonlinear dynamics without approximation,…
The idea of controlling the dynamics of spatially extended systems using a small number of localized perturbations is very appealing - such a setup is easy to implement in practice. However, when the distance between controllers generating…
We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
We introduce a ``spatial'' Lyapunov exponent to characterize the complex behavior of non chaotic but convectively unstable flow systems. This complexity is of spatial type and is due to sensitivity to the boundary conditions. We show that…
We discuss the effects of finite perturbations in fully developed turbulence by introducing a measure of the chaoticity degree associated to a given scale of the velocity field. This allows one to determine the predictability time for…