Related papers: Dynamical Origin of Power Spectra
For a paradigmatic case, the standard map, we discuss how the statistical description of the approach to equilibrium is related to the sensitivity to the initial conditions of the system. Using a numerical analysis we present an anomalous…
The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped…
The dynamics of many nanoscale biological and synthetic systems such as enzymes and molecular motors are activated by thermal noise, and driven out-of-equilibrium by local energy dissipation. Because the energies dissipated in these systems…
We address this work to investigate symbolic sequences with long-range correlations by using computational simulation. We analyze sequences with two, three and four symbols that could be repeated $l$ times, with the probability distribution…
The coupled entropy is proven to correct a flaw in the derivation of the Tsallis entropy and thereby solidify the theoretical foundations for analyzing the uncertainty of complex systems. The Tsallis entropy originated from considering…
We calculate the fluctuation of the energy of a system in Tsallis statistics following the finite heat bath canonical ensemble approach. We obtain this fluctuation as the second derivative of the logarithm of the partition function plus an…
In the absence of synaptic coupling, two or more neural oscillators may become synchronized by virtue of the statistical correlations in their noisy input streams. Recent work has shown that the degree of correlation transfer from input…
Within recently proposed scenario which explains flatness of the spectrum of scalar cosmological perturbations by a combination of conformal and global symmetries, we discuss the effect of weak breaking of conformal invariance. We find that…
We consider a system of aggregated clusters of particles, subjected to coagulation and fragmentation processes with mass dependent rates. Each monomer particle can aggregate with larger clusters, and each cluster can fragment into…
The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Benard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in…
We present a method to infer network connectivity from collective dynamics in networks of synchronizing phase oscillators. We study the long-term stationary response to temporally constant driving. For a given driving condition, measuring…
The problematic divergence of the $q$-partition function of the harmonic oscillator recently considered in \cite{plastino} is a particular case of the non-normalizabilty of the distribution function of classical Hamiltonian systems in…
The important phenomenon of "stickiness" of chaotic orbits in low dimensional dynamical systems has been investigated for several decades, in view of its applications to various areas of physics, such as classical and statistical mechanics,…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
The dynamical correlations of a model consisting of particles constrained on the line and interacting with a nearest--neighbour Lennard--Jones potential are computed by molecular--dynamics simulations. A drastic qualitative change of the…
We develop novel methods to compute auto-correlation functions, or power spectral densities, for chaotic dynamical systems generated by an inverse method whose starting point is an invariant distribution and a two-form. In general, the…
Within Tsallis' nonextensive statistics, a model is elaborated to address self-similar time series as a thermodynamic system. Thermodynamic-type characteristics relevant to temperature, pressure, entropy, internal and free energies are…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann-Gibbs…