Related papers: Globally coupled chaotic maps and demographic stoc…
We propose a general model to study the interplay between spatial dispersal and environment spatiotemporal fluctuations in metapopulation dynamics. An ecological landscape of favorable patches is generated like a L\'{e}vy dust, which allows…
Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the…
The large deviations properties of trajectory observables for chaotic non-invertible deterministic maps as studied recently by N. R. Smith, Phys. Rev. E 106, L042202 (2022) and by R. Gutierrez, A. Canella-Ortiz, C. Perez-Espigares,…
A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
A network of $N$ elements is studied in terms of a deterministic globally coupled map which can be chaotic. There exists a range of values for the parameters of the map where the number of different macroscopic configurations is very large,…
A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where {\it fluid particles} are advected by a $2d$ symplectic map…
Adaptive coupling, where the coupling is dynamical and depends on the behaviour of the oscillators in a complex system, is one of the most crucial factors to control the dynamics and streamline various processes in complex networks. In this…
Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…
We show that dynamical clustering, where a system segregates into distinguishable subsets of synchronized elements, and chimera states, where differentiated subsets of synchronized and desynchronized elements coexist, can emerge in networks…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
The collective behavior of a coupled map lattice having {\it unbounded} chaotic local dynamics is investigated through the properties of its mean field. The presence of unstable periodic orbits in the local maps determines the emergence of…
We report in details the observations of structures in coupled map lattice during its chaotic evolution, both in one and two dimension, driven by identical noise on each site (by a structure we mean a group of neighboring lattice-sites for…
The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described…
We study a class of globally coupled maps in the continuum limit, where the individual maps are expanding maps of the circle. The circle maps in question are such that the uncoupled system admits a unique absolutely continuous invariant…
The behavior of two-dimensional coupled map lattices is studied with respect to the global stabilization of unstable local fixed points without external control. It is numerically shown under which circumstances such inherent global…
Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of "causal"…