Related papers: Quantifying information loss on chaotic attractors…
We propose a general method for the construction and analysis of unweighted $\epsilon$ - recurrence networks from chaotic time series. The selection of the critical threshold $\epsilon_c$ in our scheme is done empirically and we show that…
We undertake a preliminary numerical investigation to understand how the addition of white and colored noise to a time series affects the topology and structure of the underlying chaotic attractor. We use the methods and measures of…
Recurrence networks are powerful tools used effectively in the nonlinear analysis of time series data. The analysis in this context is done mostly with unweighted and undirected complex networks constructed with specific criteria from the…
The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…
We propose a measure of divergence of probability distributions for quantifying the dissimilarity of two chaotic attractors. This measure is defined in terms of a generalized entropy. We illustrate our procedure by considering the effect of…
Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…
Information is a valuable asset for agents in socio-economic systems, a significant part of the information being entailed into the very network of connections between agents. The different interlinkages patterns that agents establish may,…
Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…
We present an analytical description of the distribution of diagonal lines in Recurrence Plots (RPs) for white noise and chaotic systems, and find that the latter one is linked to the correlation entropy. Further we identify two scaling…
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…
The retrieval abilities of spatially uniform attractor networks can be measured by the average overlap between patterns and neural states. We found that metric networks, with local connections, however, can carry information structured in…
Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease…
In principle, the state space of a chaotic attractor can be partially or wholly reconstructed from interspike intervals recorded from experiment. Under certain conditions, the quality of a partial reconstruction, as measured by the spike…
The hallmark of deterministic chaos is that it creates information---the rate being given by the Kolmogorov-Sinai metric entropy. Since its introduction half a century ago, the metric entropy has been used as a unitary quantity to measure a…
Chaotic systems make long-horizon forecasts difficult because small perturbations in initial conditions cause trajectories to diverge at an exponential rate. In this setting, neural operators trained to minimize squared error losses, while…
The aim of this paper is to investigate various information-theoretic measures, including entropy, mutual information, and some systematic measures that based on mutual information, for a class of structured spiking neuronal network. In…
In this work the information loss in deterministic, memoryless systems is investigated by evaluating the conditional entropy of the input random variable given the output random variable. It is shown that for a large class of systems the…
In this work, conditional entropy is used to quantify the information loss induced by passing a continuous random variable through a memoryless nonlinear input-output system. We derive an expression for the information loss depending on the…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…