相关论文: Global and local Complexity in weakly chaotic dyna…

Our context is Filippov systems defined on two-dimensional manifolds having a finite number of tangency points. We prove that topological transitivity is a necessary and sufficient condition for the occurrence of non-deterministic chaos…

Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is…

The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…

The motion of and interaction between phase singularities that anchor spiral waves captures many qualitative and, in some cases, quantitative features of complex dynamics in excitable systems. Being able to accurately reconstruct their…

We propose an entropy measure for the analysis of chaotic attractors through recurrence networks which are un-weighted and un-directed complex networks constructed from time series of dynamical systems using specific criteria. We show that…

Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…

We discuss a characterization of complexity based on successive approximations of the probability density describing a system by means of maximum entropy methods, thereby quantifying the respective role played by different orders of…

The notion of effective topological complexity, introduced by B{\l}aszczyk and Kaluba, deals with using group actions in the configuration space in order to reduce the complexity of the motion planning algorithm. In this article we focus on…

Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…

Under the assumption of the gluing orbit property, equivalent conditions to having zero topological entropy are investigated. In particular, we show that a dynamical system has the gluing orbit property and zero topological entropy if and…

Time correlated fluctuations interacting with a spatial asymmetry potential are sufficient conditions to give rise to transport of Brownian particles. The transfer of information coming from the nonequilibrium bath, viewed as a source of…

We introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine systems likely to experience chaotic itinerancy by means of…

We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…

Complexity is a measure of information content. Crystalline materials are not complex systems because their structures can be represented tersely using the language of crystallography. Disordered materials are also structurally simple if…

We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum…

Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…

Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…

Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…

Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…

One of the central challenges facing modern neuroscience is to explain the ability of the nervous system to coherently integrate information across distinct functional modules in the absence of a central executive. To this end Tononi et al.…