Search results for "Coupled map lattice"
showing 10 items of 13 documents
Weakly coupled map lattice models for multicellular patterning and collective normalization of abnormal single-cell states
2017
We present a weakly coupled map lattice model for patterning that explores the effects exerted by weakening the local dynamic rules on model biological and artificial networks composed of two-state building blocks (cells). To this end, we use two cellular automata models based on: (i) a smooth majority rule (model I) and (ii) a set of rules similar to those of Conway's Game of Life (model II). The normal and abnormal cell states evolve according with local rules that are modulated by a parameter $\kappa$. This parameter quantifies the effective weakening of the prescribed rules due to the limited coupling of each cell to its neighborhood and can be experimentally controlled by appropriate e…
Pattern formation and spatial correlation induced by the noise in two competing species
2004
We analyze the spatio-temporal patterns of two competing species in the presence of two white noise sources: an additive noise acting on the interaction parameter and a multiplicative noise which affects directly the dynamics of the species densities. We use a coupled map lattice (CML) with uniform initial conditions. We find a nonmonotonic behavior both of the pattern formation and the density correlation as a function of the multiplicative noise intensity.
Nonmonotonic behavior of spatiotemporal pattern formation in a noisy Lotka-Volterra system
2004
The noise-induced pattern formation in a population dynamical model of three interacting species in the coexistence regime is investigated. A coupled map lattice of Lotka-Volterra equations in the presence of multiplicative noise is used to analyze the spatiotemporal evolution. The spatial correlation of the species concentration as a function of time and of the noise intensity is investigated. A nonmonotonic behavior of the area of the patterns as a function of both noise intensity and evolution time is found.
Construction of chaotic dynamical system
2010
The first‐order difference equation xn+ 1 = f(xn ), n = 0,1,…, where f: R → R, is referred as an one‐dimensional discrete dynamical system. If function f is a chaotic mapping, then we talk about chaotic dynamical system. Models with chaotic mappings are not predictable in long‐term. In this paper we consider family of chaotic mappings in symbol space S 2. We use the idea of topological semi‐conjugacy and so we can construct a family of mappings in the unit segment such that it is chaotic. First published online: 09 Jun 2011
Short chaotic strings and their behaviour in the scaling region
2008
Coupled map lattices are a paradigm of higher-dimensional dynamical systems exhibiting spatio-temporal chaos. A special case of non-hyperbolic maps are one-dimensional map lattices of coupled Chebyshev maps with periodic boundary conditions, called chaotic strings. In this short note we show that the fine structure of the self energy of this chaotic string in the scaling region (i.e. for very small coupling) is retained if we reduce the length of the string to three lattice points.
Horizontal visibility graphs: exact results for random time series
2009
The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows us to apply methods of complex network theory for characterizing time series. In this work we present the horizontal visibility algorithm, a geometrically simpler and analytically solvable version of our former algorithm, focusing on the mapping of random series (series of independent identically distributed random variables). After presenting some properties of the algorithm, we present exact results on the topological properties of graphs associated with random series, namely, the degree distribution, the clustering coefficient, and the mean path length. We sh…
Moment Equations for a Spatially Extended System of Two Competing Species
2005
The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulat…
Nonmonotonic Pattern Formation in Three Species Lotka-Volterra System with Colored Noise
2005
A coupled map lattice of generalized Lotka-Volterra equations in the presence of colored multiplicative noise is used to analyze the spatiotemporal evolution of three interacting species: one predator and two preys symmetrically competing each other. The correlation of the species concentration over the grid as a function of time and of the noise intensity is investigated. The presence of noise induces pattern formation, whose dimensions show a nonmonotonic behavior as a function of the noise intensity. The colored noise induces a greater dimension of the patterns with respect to the white noise case and a shift of the maximum of its area towards higher values of the noise intensity.
Stochastic dynamics and mean field approach in a system of three interacting species
2008
The spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied. To describe the spatial distributions of the species we use a model based on Lotka-Volterra equations. A correlated dichotomous noise acts on \beta, the interaction parameter between the two preys, and a multiplicative white noise affects directly the dynamics of each one of the three species. We study the time behaviour of the three species in single site for different values of the multiplicative noise intensity, finding noise-induced oscillations of the three species densities with an anticorrelated behaviour of the two preys. Afterwar…
Role of the Colored Noise in Spatio-Temporal Behavior of Two Competing Species
2005
We study the spatial distributions of two randomly interacting species, in the presence of an external multiplicative colored noise. The dynamics of the ecosystem is described by a coupled map lattice model. We find a nonmonotonic behavior in the formation of large scale spatial correlations as a function of the multiplicative colored noise intensity. This behavior is shifted towards higher values of the noise intensity for increasing correlation time of the noise.