Generation of 3and 4-dimensional graphics is discussed in the context of stellarator ballooning mode theory and the nonlinear dynamics of a 4-dimensional symplectic map (two coupled area-preserving maps). These provide case studies for informally reviewing the history of some commercially available visualization software for personal computers (Macintosh and Windows) developed by US small-to-me...

The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open ow is investigated and shown to be extremely rich. For medium and large coupling strengths, we nd spatially periodic, quasiperiodic and chaotic patterns with temporal periodicity and analyze their stability with the help of a newly introduced spatial map. Criteria are established fo...

We propose a secure algorithm for direct encryption and decryption of digital images with chaotic map lattices. The basic idea is to convert, pixel by pixel, the image color to chaotic logistic maps one-way coupled by initial conditions. After small numbers of iterations and cycles, the image becomes indistinguishable due to inherent properties of chaotic systems. Since the maps are coupled, th...

In this paper, an implementation of digital image encryption scheme based on one dimensional logistic map is proposed. The chaotic cryptography technique concentrates in general on the symmetric key cryptographic technique. In the proposed algorithm, a random key table lookup criterion was combined with a one-dimensional chaotic map were used for high degree 2-stage security image encryption wh...

In this paper, analytic solutions of two-dimensional coupled Burgers' equations are obtained by the Homotopy analysis and the Homotopy Pad$acute{e}$ methods. The obtained approximation by using Homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by $[m,m]$ Homotopy Pad$acute{e...

In this paper, the D3 dihedral logistic map of fractional order is introduced. The presents a symmetry D3. It numerically shown that construction and interpretation bifurcation diagram versus requires special attention. system stability determined problem hidden attractors analyzed. Furthermore, analytical numerical results show chaotic attractor integer order, with symmetries, looses its in fr...