Related papers: Analytical Approach for Piecewise Linear Coupled M…
A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity…
We construct a mixing continuous piecewise linear map on [-1,1] with the property that a two-dimensional lattice made of these maps with a linear north and east nearest neighbour coupling admits a phase transition. We also provide a…
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
Synchronization among globally coupled, chaotic map lattices can be related to stable periodic windows in isolated chaotic maps. This relation provides a simple predictive tool for the understanding of complicated behavior in coupled…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…
We consider a lattice of weakly coupled expanding circle maps. We construct, via a cluster expansion of the Perron-Frobenius operator, an invariant measure for these infinite dimensional dynamical systems which exhibits space-time-chaos.
In this article, we have studied a 1D map, which is formed by combining the two well-known maps i.e. the tent and the logistic maps in the unit interval i.e. [0, 1]. The proposed map can behave as the piecewise smooth or non-smooth maps…
We obtain exact analytical results for lattices of maps with couplings that decay with distance as $r^{-\alpha}$. We analyze the effect of the coupling range on the system dynamics through the Lyapunov spectrum. For lattices whose elements…
We study a certain class of classical one dimensional piecewise linear maps. For these systems we introduce an infinite family of Markov partitions into equal cells. The symbolic dynamics generated by these systems is described by…
In lattice gauge theory, there exist field transformations that map the theory to the trivial one, where the basic field variables are completely decoupled from one another. Such maps can be constructed systematically by integrating certain…
The logistic map is a paradigmatic dynamical system originally conceived to model the discrete-time demographic growth of a population, which shockingly, shows that discrete chaos can emerge from trivial low-dimensional non-linear dynamics.…
For a transitive countably piecewise monotone Markov interval map we consider the question whether there exists a conjugate map of constant slope. The answer varies depending on whether the map is continuous or only piecewise continuous,…
The phase diagram of the coupled sine circle map lattice exhibits a variety of interesting phenomena including spreading regions with spatiotemporal intermittency, non-spreading regions with spatial intermittency, and coherent structures…
The coupled (chaotic) map lattices (CMLs) characterizes the collective dynamics of a spatially distributed system consisting of locally or globally coupled maps. The current research on the dynamic behavior of CMLs is based on the framework…
The infinite discrete stable Boltzmann maps are "heavy-tailed" generalisations of the well-known Uniform Infinite Planar Quadrangulation. Very efficient tools to study these objects are Markovian step-by-step explorations of the lattice…
Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The…
For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…
We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete,…
This article is concerned with analytic Hamiltonian dynamical systems in infinite dimension in a neighborhood of an elliptic fixed point. Given a quadratic Hamiltonian, we consider the set of its analytic higher order perturbations. We…