In this letter, after reviewing the main points of the chaotic trigonometric maps and the coupled map lattices, we introduce the scheme of chaos-based image encryption based on coupled map lattices. The scheme decreases periodic effect of the ergodic dynamical systems in the chaos-based image encryption. To evaluate the security of the encrypted image of this scheme, the key space analysis, the...

In this paper, we intend to show that the flocking phenomenon observed in many animal species behaviors, may be modeled as a synchronization process occurring within entity states. Although flocking has been widely studied and simulated in Swarm Intelligence, few works mention synchronization as a key aspect of the problem and model it properly. This paper proposes a modeling in terms of a reac...

We consider three systems that are spatially one-dimensional and are discretized in space and time: i) cellular automata proposed by Wolfram; ii) a system that has been used as a prototype for coupled map lattices; and iii) a coupled map lattice that provides a simple description of earthquakes. Chaotic modes of these systems can be made periodic by external forcing at points equidistant in spa...

We introduce a new coupled map lattice model in which the weak interaction takes place via rare “collisions”. By “collision” we mean a strong (possibly discontinuous) change in the system. For such models we prove uniqueness of the SRB measure and exponential space-time decay of correlations.

Density fluctuations in traffic current are studied by computer simulations using the deterministic coupled map lattice model on a closed single-lane circuit. By calculating a power spectral density of temporal density fluctuations at a local section, we find a power-law behavior, ∼ 1/f, on the frequency f , in non-congested flow phase. The distribution of the headway distance h also shows the ...

For a class of 1-dimensional lattice dynamical systems we prove the existence of periodic traveling waves with prescribed speed and arbitrary period. Then we study asymptotic behaviour of such waves for big values of period and show that they converge, in an appropriate topology, to a solitary traveling wave.

In this paper, we study the existence and stability of traveling waves in lattice dynamical systems, in particular, in lattice ordinary di erential equations (lattice ODE's) and in coupled map lattices (CML's). Instead of employing the moving coordinate approach as for partial di erential equations, we construct a local coordinate system around a traveling wave solution of a lattice ODE, analog...

Multilinear maps have become popular tools for designing cryptographic schemes since a first approximate realisation candidate was proposed by Garg, Gentry and Halevi (GGH). This construction was later improved by Langlois, Stehlé and Steinfeld who proposed GGHLite which offers smaller parameter sizes. In this work, we provide the first implementation of such approximate multilinear maps based ...

This paper is concerned with a lattice dynamical system modeling the evolution of susceptible and infective individuals at discrete niches. We prove the existence of traveling waves connecting the disease-free state to non-trivial leftover concentrations. We also characterize the minimal speed of traveling waves and we prove the non-existence of waves with smaller speeds.