The dynamics of globally coupled map lattices can be described in terms of a nonlinear Frobenius–Perron equation in the limit of large system size. This approach allows for an analytical computation of stationary states and their stability. The complete bifurcation behaviour of coupled tent maps near the chaotic band merging point is presented. Furthermore the time independent states of coupled...

The aim of this paper is to increase security of double random phase encoding (DRPE) method using chaos theory and hash function for phase mask generation. DRPE encodes the input image by the use of two keys which are random phase masks. Having these keys, the original image can be easily obtained with the reverse process, called decoding. To enhance the system’s security, instead of sending ra...

We analyze the size limits of coupled map lattices with diffusive coupling at the crossover of low-dimensional to high-dimensional chaos. We investigate the existence of standing-wave-type periodic patterns, within the low-dimensional limit, in addition to the stable synchronous chaotic states depending upon the initial conditions. Further, we bring out a controlling mechanism to explain the em...

If one isolated species is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species can be expressed by a coupled system of two discrete logistic equations. As three basic relationships between two species are present in Nature, namely symbiosis, predator-prey and competition, three different models are obtained. Each model is a cubic two-...

An increasing number of collaborative learning environments is based on shared workspace systems using two-dimensional graph-structured visual representations such as argumentation networks and concept maps. We propose an integrated framework that allows for flexibly specifying a wide range of visual languages and plugging in components for operational semantics, adequate feedback and intellige...

A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis qexponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting family of q-logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors – a phenomenon rare in one dim...

We propose the deep-zoom analysis of composition logistic map and tent map, which are well-known discrete one-dimensional chaotic maps. The technique transforms each point a given orbit by removing first k-digits after decimal separator. found that pseudo-random qualities as number generator (PRNG) improve k parameter increases. This was evidenced fact it successfully passed randomness tests ev...