We show that the infinite-dimensional representation of the recently introduced logistic algebra can be interpreted as a nontrivial generalization of the Heisenberg or oscillator algebra. This allows us to construct a quantum Hamiltonian having the energy spectrum given by the logistic map. We analyze the Hamiltonian of a solid whose collective modes of vibration are described by this generaliz...

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...

Chaos has three important dynamic properties : the sensitive dependence on initial conditions, the intrinsic stochastic property and ergodicity. So it was applied to optimization problems. In most optimization methods such as the COA [1] and [4], variables chaos generated by different types of applications such as the Logistic, the application Tent, Lozi, Ikeda and others have shown very intere...

In this paper, we present a novel approach to create the new chaotic map and propose an improved image encryption scheme based on it. Compared with traditional classic one-dimensional chaotic maps like Logistic Map and Tent Map, this newly created chaotic map demonstrates many better chaotic properties for encryption, implied by a much larger maximal Lyapunov exponent. Furthermore, the new chao...

Compressive sensing uses simultaneous sensing and compression to provide an efficient image acquisition technique and it has been demonstrated in optical and electrical image sensors. To guarantee exact recovery from sparse measurements, specific sensing matrix, which satisfies the Restricted Isometry Property (RIP), should be well chosen. Toeplitz-structured chaotic sensing matrix constructed ...

Recently, binary sequences generated by chaotic maps have been widely studied. In particular, the logistic map is used as one of the chaotic map. However, if the logistic map is implemented by using finite precision computer arithmetic, rounding is required. In order to avoid rounding, Miyazaki, Araki, Uehara and Nogami proposed the logistic map over finite fields, and show some properties of s...

We report on the definition and characteristics of nodes in the chaotic region of bifurcation diagrams in the case of 1D mono-parametrical and S-unimodal maps, using as guiding example the logistic map. We examine the arrangement of critical curves, the identification and arrangement of nodes, and the connection between the periodic windows and nodes in the chaotic zone. We finally present seve...

The extent of chaos and the suppressory role of Coulomb repulsion in the chaotic dynamics associated with nonsteady finite-amplitude electroconvection is revisited in the context of dynamical systems. Specifically, it is theoretically demonstrated that the threshold value of the charge density taming the heteroclinic chaos associated with laminar chaotic mixing depends on the sinusoidal perturb...

This research work describes a nine-term 3-D novel chaotic system with four quadratic nonlinearities. First, this work describes the dynamic analysis of the novel chaotic system and qualitative properties of the novel chaotic system are derived. The Lyapunov exponents of the nine-term novel chaotic system are obtained as L1 1⁄4 9:45456; L2 1⁄4 0 and L3 1⁄4 30:50532. Since the maximal Lyapunov e...