We model tree migration with a coupled map lattice and study the dynamics of the moving front. We show that when the maximal dispersal distance is finite and the spatial redistribution pattern remains unchanged in time, the moving front will always approach an asymptotic state: a travelling wave. We also show that when the climate becomes more favorable to growth or germination, the front at an...

Let L be a lattice and let L1, L2 be sublattices of L. Let be a congruence relation of L1. We extend to L by taking the smallest congruence of L containing . Then we restrict to L2, obtaining the congruence L2 of L2. Thus we have de ned a map ConL1 ! ConL2. Obviously, this is an isotone 0-preservingmap of the nite distributive lattice ConL1 into the nite distributive lattice ConL2. The main res...

The scaling hypothesis for the coupled chaotic map lattices (CML) is formulated. Scaling properties of the CML in the regime of extensive chaos observed numerically before is justified analytically. The asymptotic Liapunov exponents spectrum for coupled piece-wise linear chaotic maps is found.

In this paper, we study chaotic synchronization in 1D lattices of two-variable maps coupled with one variable. We give a rigourous proof for the occurrence of chaotic synchronization of spatially homogeneous solutions in such coupled map lattices (CMLs) of lattice size n = 4 with suitable coupling coefficients. For the case of lattice size n > 4, we demonstrate numerical results of synchronized...

We prove the existence of a unique SRB measure for a wide range of multidimensional weakly coupled map lattices. These include piecewise expanding maps with diffusive coupling.

We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle properly, and the maps are coupled to each other through the headway distance. By simulating the model, we obtain a plot of the flow against the concentration...

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 admissibility condition, approximations of the corresponding symbolic systems are obtained. These approximations imply that the topological entropy is located b...

Let Φ be an irreducible crystallographic root system with Weyl group W , coroot lattice Q̌ and Coxeter number h. Recently the second named author defined a uniform W -isomorphism ζ between the finite torus Q̌/(mh + 1)Q̌ and the set of non-nesting parking functions Park(Φ). If Φ is of type An−1 and m = 1 this map is equivalent to a map defined on labelled Dyck paths that arises in the study of the ...

We define a class 3 of topological dynamical systems, which are left invariant by coupled map lattice constructions. ‘fhis class .F has the property that if the coupling of the systems is sufficiently weak and (M, f) contains a hyperbolic set, ‘hen the new system $( M, f) obtained by the coupled map lattice construction has a hyperbolic set too. The coupled map attice construction, map 4, can b...