Related papers: Sensitivity to Initial Conditions and Nonextensivi…
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition…
Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in…
Evolutionary dynamics in an uncorrelated rugged fitness landscape is studied in the framework of Eigen's molecular quasispecies model. We consider the case of strong selection, which is analogous to the zero temperature limit in the…
In hydrodynamics, the momentum distribution of particles at the end of the evolution is completely determined by initial conditions. We study quantitatively to what extent anisotropic flow is determined by predictors such as the initial…
Using a Boltzmann equation, we investigate the nonequilibrium dynamics of nonperturbative fluctuations within the context of Ginzburg-Landau models. As an illustration, we examine how a two-phase system initially prepared in a homogeneous,…
We describe a method to extract from experimental data the important dynamical modes in spatio-temporal patterns in a system driven out of thermodynamic equilibrium. Using a novel optical technique for controlling fluid flow, we create an…
Spatial extent is a complicating factor in mathematical biology. The possibility that an action at point A cannot immediately affect what happens at point B creates the opportunity for spatial nonuniformity. This nonuniformity must change…
We present a general growth model based on non-extensive statistical physics is presented. The obtained equation is expressed in terms of nonadditive $q$ entropy. We show that the most common unidimensional growth laws such as power law,…
We study the totally asymmetric simple exclusion process (TASEP) on $\mathbb{Z}$ with a general initial condition and a deterministically moving wall in front of the particles. Using colour-position symmetry, we express the one-point…
In this work a three-states cellular automaton proposed to describe part of a biological immune system is revisited. We obtain the dynamic critical exponent $z$ of the model by means of a recent technique that mixes different initial…
We present several recent results concerning the transition between quantum and classical mechanics, in the situation where the underlying dynamical system has an hyperbolic behaviour. The special role of invariant manifolds will be…
We address the problem of parameter estimation in models of systems biology from noisy observations. The models we consider are characterized by simultaneous deterministic nonlinear differential equations whose parameters are either taken…
We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the…
The dynamics of the convergence to the critical attractor for the logistic map is investigated. At the border of chaos, when the Liapunov exponent is zero, the use of the non-extensive statistical mechanics formalism allows to define a weak…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…
We present a detailed study of the effects of the initial distribution on the kinetic evolution of the irreversible reaction A+B -> 0 in one dimension. Our analytic as well as numerical work is based on a reaction-diffusion model of this…
Biological evolution of a population is governed by the fitness landscape, which is a map from genotype to fitness. However, a fitness landscape depends on the organisms environment, and evolution in changing environments is still poorly…
Power-law sensitivity to initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity as prescribed in the generalized statistics recently…
Critical exponents of the infinitely slowly driven Zhang model of self-organized criticality are computed for $d=2,3$ with particular emphasis devoted to the various roughening exponents. Besides confirming recent estimates of some…