Nowadays the question `what is complexity?' is a challenge to be answered. This question is triggering a great quantity of works in the frontier of physics, biology, mathematics and computer science. Even more when this century has been told to be the century of Complexity. Although there seems to be no urgency to answer the above question, many different proposals that have been developed to t...

In this paper, we investigate the properties of join and meet preserving maps in complete residuated lattice using Zhang’s the fuzzy complete lattice which is defined by join and meet on fuzzy posets. We define L-upper (resp. L-lower) approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between L-upper (resp. L-l...

We consider coupled map lattices of hyperbolic type, i.e., chains of weakly interacting hyperbolic sets (attractors) over multi-dimensional lattices. We describe thermodynamic formalism of the underlying spin lattice system and then prove existence, uniqueness, mixing properties, and exponential decay of correlations of equilibrium measures for a class of Holder continuous potential functions ...

We describe the transfer operator approach to coupled map lattices (CML) in cases where the local map is expanding but has no Markov partition (e.g. a general tent map). The coupling is allowed to be non-local, but the total innuence of all sites j 6 = i on site i must be small. The main technical tool are lattice-size independent estimates of Lasota-Yorke type which show that the transfer (Per...

By choosing a dynamical system with d different couplings, one can rearrange a system based on the graph with given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a relation between the vertexes. Based on the E0 transverse projection operator. We addressed synchronization problem of an array of the linearly coupled map la...

Phase synchronized states can emerge in the collective behavior of an ensemble of chaotic coupled map lattices, due to a mean field interaction. This type of interaction is responsible for synchronized chaotic global activity of the lattices, while the local activity of each map remains unsynchronized. The resulting collective dynamics is called “weak synchronization.” The transition to such a ...

This work reports a systematic investigation of the distribution of periodic and aperiodic patternevolution in rings of diffusively coupled quadratic maps. Our main motivation here is the wish to investigate whether lattices of coupled maps can be effectively used to simulate a plethora of phenomena associated with climatic variability and change. Presently, simulations of these phenomena reduc...

Beyond the uncoupled regime, the rigorous description of the dynamics of (piecewise) expanding coupled map lattices remains largely incomplete. To address this issue, we study repellers of periodic chains of linearly coupled Lorenz-type maps which we analyze by means of symbolic dynamics. Whereas all symbolic codes are admissible for sufficiently small coupling intensity, when the interaction s...

We consider the sum of dichromatic polynomials over non-separable rooted planar maps, an interesting special case of which is the enumeration of such maps. We present some known results and derive new ones. The general problem is equivalent to the q-state Potts model randomized over such maps. Like the regular ferromagnetic lattice models, it has a first-order transition when q is greater than ...

A lattice tetrahedron T ⊂ R3 is a tetrahedron whose four vertices are all in the lattice Z3. Lattice tetrahedra are preserved by those affine linear maps of the form ~v 7→ A~v +~b, such that A is an element of GL(3,Z) and ~b is an element of the lattice Z3. Such affine linear maps are called unimodular maps. We say that a lattice tetrahedron whose barycentre is its only non-vertex lattice point...