Related papers: Emergence of chaotic behaviour in linearly stable …
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…
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…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…
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 investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, we quantify the divergence of initially…
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic…
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…
Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…
Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…
Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When…
Recently, a concept of deterministic and stochastic turbulence has been introduced based on experiments with a boundary layer. In these experiments, the flow was driven with controlled random perturbation; in addition, natural ambient noise…
Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…
We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We…
The possibility of complicated dynamic behaviour driven by non-linear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility…
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to…