Coupled map lattices have been widely used as models in several fields of physics, such as chaotic strings, turbulence, and phase transitions, as well as in other disciplines, such as biology (ecology, evolution) and information processing. This paper investigates properties of periodic orbits in two coupled Tchebyscheff maps. Then zeta function cycle expansions are used to compute dynamical av...

In this paper we examine assets price deviation in a multi-market system with heterogeneous investors in each market. Coupled map lattices (CML) is introduced to the market maker framework. It results in market cluster sharing the same sign of deviation in the chaotic interval. Distribution plots are applied to understand the deviation persistence enhancement from the coupling e¤ect. Besides th...

We use one-dimensional coupled lattice maps (CMLs) to generate sounds that reflect spatial organization and temporal evolution of these dynamics started from a random initial configuration corresponding to uncorrelated noise. In many instances, the process approaches an equilibrium, which generates a sustained tone. The pitch of this tone is proportional to the lattice size, so the CML behaves ...

Weakly interacting lattices of coupled maps can be modeled as ordinary coupled map lattices separated from each other by boundary regions with small coupling parameters. We demonstrate that such weakly interacting lattices can nevertheless have unexpected and striking effects on each other. Under specific conditions, particular stability properties of the lattices are significantly influenced b...

In this paper, an image encryption algorithm based on DNA random coding and random operation combined with chaotic map is proposed. In order to produce sequences with more chaotic characteristics, a new spatiotemporal chaotic system is proposed by employing the Tent-Sine system (TSS) in the coupled map lattice (CML). SHA-256 hash of the plain image is used to generate secret keys. The Lorenz Ma...

In this paper, a discrete version of a reaction-diffusion equation, also known as coupled map lattice (CML), which corresponds to the Turing model of morphogenesis is studied. It is shown that CML possesses a hyperbolic property displaying a type of spatio-temporal chaos. Throughout a mathematical background of hyperbolic properties in lattice dynamical systems which are related to spatio-tempo...

In this article the authors discuss a new method of the so-called complex networks dynamics and its visualization by means of so called coupled map lattices method. The main aim of this article is to investigate whether it is possible to visualize complex network dynamics by means of the same method that is used to model spatiotemporal chaos. The authors suggest using coupled map lattices syste...

A type of coupled map lattice (CML) is considered in this paper. What we want to do is to define the form of a traveling wave solution and to reveal its existence. Due to the infinite property of the problem, we have tried the periodic case, which can be dealt with on a finite set. The main approach for our study is the implicit existence theorem. The results indicate that if the parameters of ...

Motivated by the computations done in [9], where I introduced and discussed what I called the groupoid of generalized gauge transformations, viewed as a groupoid over the objects of the category BunG,M of principal G-bundles over a given manifold M , I develop in this paper the same ideas for the more general case of principal G-bundles or principal bundles with structure groupoid G, where now ...

Properties of intermediate-range coupling are studied in 1-dimensional coupled map lattices (CMLs). Phase diagrams have been constructed which describe the relationship between the range of coupling and coupling strength. A delicate low-dimensional attractor is emerging for non-global interactions in the case of weak coupling, while the leading Lyapunov exponent is a large positive number.