Related papers: A "metric" complexity for weakly chaotic systems
A practical measure for the complexity of sequences of symbols (``strings'') is introduced that is rooted in automata theory but avoids the problems of Kolmogorov-Chaitin complexity. This physical complexity can be estimated for ensembles…
Using the tools of Differential Geometry, we define a new <<fast>> chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e. "quickly") than the usual tools, like Lyapunov Characteristic Numbers…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
The LMC complexity, an indicator of complexity based on a probabilistic description, is revisited. A straightforward approach allows us to establish the time evolution of this indicator in a near-equilibrium situation and gives us a new…
Weak chaos in high-dimensional conservative systems can be characterized through sticky effect induced by invariant structures on chaotic trajectories. Suitable quantities for this characterization are the higher cummulants of the finite…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…
On account of a greater need for understanding the complexity of time series like physiological time series, financial time series, and many more that enter into picture for their inculpation with real-world problems, several complexity…
We evaluate new complexity measures on the symbolic dynamics of coupled tent maps and cellular automata. These measures quantify complexity in terms of $k$-th order statistical dependencies that cannot be reduced to interactions between…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where other properties such as Lyapunov exponents are difficult to define in an observer independent manner.…
Generic dynamical systems have `typical' Lyapunov exponents, measuring the sensitivity to small perturbations of almost all trajectories. A generic system has also trajectories with exceptional values of the exponents, corresponding to…
We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the…
We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…
Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…
In recent studies, new measures of complexity for nonlinear systems have been proposed based on probabilistic grounds, as the LMC measure (Phys. Lett. A {\bf 209} (1995) 321) or the SDL measure (Phys. Rev. E {\bf 59} (1999) 2). All these…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…