The circle map in one and two dimensions is studied. Both its stability and synchronization , using a bounded control and persistence, are discussed. This work is expected to be applicable in ecology where spatial effects are known to be important. Also, it will be relevant to systems where delay effects are not negligible.

The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...

the paper deals with special types of $l$-ordered sets, $l$-fuzzy complete lattices, and fuzzy directed complete posets.first, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $l$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $l$-fuzzy complete lattice $(p;e)$, then the least fixpoint of $f$ is meet of ...

Encryption is an important issue in information security which is usually provided using a reversible mathematical model. Digital image as a most frequently used digital product needs special encryption algorithms. This paper presents a new encryption algorithm high security for digital gray images using genetic algorithm and Lattice Map function. At the first the initial value of Logistic Map ...

In recent years, the advancement of digital technology has led to an increase in data transmission on the Internet. Security of images is one of the biggest concern of many researchers. Therefore, numerous algorithms have been presented for image encryption. An efficient encryption algorithm should have high security and low search time along with high complexity.DNA encryption is one of the fa...

We describe the emergence of phase clustering and collective behaviors in an ensemble of chaotic coupled map lattices, due to a mean field interaction. This kind of interaction is responsible for the appearence of a collective state, wherein the mean field evolution of each lattice undergoes a periodic behavior in space. We analyze the transition to such a state in an ensemble of one-dimensiona...

Two-dimensional coupled map lattices display, in a specific parameter range, a stable phase (quasi-) periodic in both space and time. With small changes to the model parameters, this stable phase develops spontaneous eruptions of nonperiodic behavior. Although this behavior itself appears irregular, it can be characterized in a systematic fashion. In particular, parameter-independent features o...

In relation to spatiotemporal intermittency, as it can be observed in coupled map lattices, we study the stability of different wavelengths in competition. Introducing a two dimensional map, we compare its dynamics with the one of the whole lattice. We conclude a good agreement between the two. The reduced model also allows to introduce an order parameter which combines the diffusion parameter ...

The main part of the theory of residuated groupoids has been technical and the results apparently diverse in nature. However P. Dubreil and R. Croisot [5], using the concepts of residuated and residual maps, were able to present the basic properties of residuals in a simple unified manner. R. Croisot [3] carried on this study. In this paper we build a theory of residuated and residual maps whic...