[en] In this paper, we propose a new hyperchaotic complex system and systematically study its basic dynamic characteristics such as dissipation, Lyapunov exponent, attractor, parameter changes, and $Poincar\stackrel{´<!--\; ??\; -->}{e}$ cross-section. The system is based on the complex Lorenz chaotic system, and the chaotic system has higher dimensionality and more parameters than complex Lorenz system. We provide a general method for constructing complex chaotic systems. We use the state linear feedback method to realize the synchronization control of the chaotic system as the driving system and the response system and simulate all of the systems by Simulink. The chaotic system and its synchronization simulation are simulated by Simulink to verify their hardware feasibility. (paper)

[en] We study in detail the trajectories, ordered and chaotic, of two entangled Bohmian qubits when their initial preparation satisfies (or not) Born’s rule for various amounts of quantum entanglement. For any non zero value of entanglement ordered and chaotic trajectories coexist and the proportion of ordered trajectories increases with the decrease of the entanglement. In the extreme cases of zero and maximum entanglement we have only ordered and chaotic trajectories correspondingly. The chaotic trajectories of this model are ergodic, for any given value of entanglement, namely the limiting distribution of their points does not depend on their initial conditions. Consequently it is the ratio between ordered and chaotic trajectories which is responsible for the dynamical establishment (or not) of Born’s rule. (paper)

[en] Chaos is widely used in secure communication and cryptography due to its randomness, unpredictability, non-periodicity and high sensitivity to initial values and parameters. However, there are many risks in some existing chaotic image encryption algorithms because they use the the chaotic map without complex dynamic characteristics. To overcome these weaknesses, in this paper introduced an improved Hénon map, and the dynamic analysis results show that the improved Hénon map has more rich chaotic behaviors and better complexity. In addition, we designed a color image encryption scheme using the improved Hénon sequences. For this encryption algorithm, color image is divided into R, G, B primary colors, then R, G, B primary colors are scrambled and diffused by the improved Hénon sequences. The simulation results illustrate that color image encryption algorithm security is advanced by usingimproved Hénon map. (paper)

[en] The kicked rotor (KR) is one of the basic models in connection with chaos and quantum chaos. A possible application of an attosecond pulse train as a kicking field in the KR is theoretically examined for the first time. This version of the KR is denoted as an atto-KR. It seems to be the most realistic version of the KR because it takes into account the real form of the kicking field as it appears in the experiments. The atto-KR is investigated from the classical and the quantum aspects. In the classical case, a new map instead of the Chirikov standard map is proposed. It may be useful in appropriate experiments with the classical chaos. In the quantum case, the atto-KR gives satisfactory results. Phenomena such as dynamical localization and quantum resonances appear in the undisturbed form. It may be also used for examining the influence of the quantum effects on classical chaos and diffusion. (paper)

[en] This paper introduces a new hyperchaotic oscillator base on a new boundary-restricted Hewlett-Packard memristor model. Firstly, the complex system is designed based on a memristor-based hyperchaotic real system, and its properties are analyzed by means of Lyapunov exponents, Lyapunov dimension and phase portraits diagrams. Secondly, a simple feedback control based on the minimum variance control technique is designed to stabilize the hyperchaotic oscillator system, which is one of the new developed approaches for controlling the chaos in high-dimensional hyperchaotic systems. In this method, the time series variance is considered for designing and calculating the state feedback control gain. Furthermore, the state feedback control is designed so that to minimize the variance as a cost function, followed by developing an online optimization technique using the particle swarm optimization method in order to calculate the state feedback control based on the minimum variance strategy. Then, the application of this method is examined on a hyperchaotic memristor-based oscillator. Finally, the sensitivity of the proposed method is evaluated in different initial conditions that greatly influence the hyperchaotic dynamics. Considering that the optimization is online, simulation results show highly good effectiveness of the presented technique in controlling the chaos in high-dimensional hyperchaotic oscillators (paper)

[en] In this paper, we apply Andreev’s reflection to study the sub-gap coherent transport properties for a quantum dot attached to normal metal and superconductor reservoirs via non-ideal leads. We use the random matrix theory to obtain numerically the conductance and shot noise power probability densities varying the transparencies and the number of open scattering channels in each lead for the three Wigner–Dyson ensembles. We obtain results from the extreme quantum limit (where the conductance is of the order of 2e ²/h, the quantum of conductance) to the semiclassical regime (conductance much larger than 2e ²/h). We observe the appearance of non-analyticities in these probability densities and an interesting invariance break under the operation of exchanging the lead labels when time-reversal symmetry is absent. (paper)

[en] In this paper, we consider the difference synchronization for different chaotic maps with different dimensions using three scaling matrices. The proposed method allows us to study difference synchronization of two master discrete-time chaotic systems with dimension $n$ and one response discrete-time chaotic system with dimension $m.$ Based on the Lyapunov stability theory and stability property of linear discrete-time systems, controllers are derived to achieve the difference synchronization among three nonidentical discrete-time chaotic systems with different dimensions in two cases: $n<<!--\; <\; -->m$ and $n><!--\; >\; -->m.$ For the case $n<<!--\; <\; -->m,$ 2D Fold map and 2D Hénon map are used as the master systems, and the 3D Hitzl-Zele map is chosen as the slave system to simulate the difference synchronization. For the case $n><!--\; >\; -->m,$ 3D Stefanski map and 3D Baier-Klein map are adopted as the master systems, and 2D Lorenz discrete-time chaotic system is used as the slave system during the simulation. The numerical simulations illustrate the effectiveness and feasibility of the proposed method. (paper)

[en] We consider the problem of a semiclassical description of quantum chaotic transport, when a tunnel barrier is present in one of the leads. Using a semiclassical approach formulated in terms of a matrix model, we obtain transport moments as power series in the reflection probability of the barrier, whose coefficients are rational functions of the number of open channels M. Our results are therefore valid in the quantum regime and not only when M ≫ 1. The expressions we arrive at are not identical with the corresponding predictions from random matrix theory, but are in fact much simpler. Both theories agree as far as we can test. (paper)

[en] This paper proposes a fractional-order cellular neural network (CNN) chaotic system for image encryption algorithm to explore the application of fractional-order CNN hyperchaotic system in chaotic secure communication. Firstly, a fractional-order CNN hyperchaotic system is defined based on CNN hyperchaotic system. The numerical solutions of the fractional-order CNN hyperchaotic system are calculated by Adomian decomposition algorithm. The dynamic characteristics of the of the fractional-order CNN hyperchaotic system are analyzed. Then to verify the image encryption application of the fractional-order CNN hyperchaotic system, we designed an image encryption scheme through fractional-order CNN hyperchaotic sequence, the principle of symmetry of main diagonal of matrix and XOR operation. Finally, the results illustrate that the fractional-order CNN hyperchaotic sequence has good randomness, which show that the fractional-order CNN hyperchaotic system more suitable for chaotic secure communication applications. The security performances of the algorithm show that the designed algorithm can effectively encrypt and decrypt image, and has better security performance. (paper)

[en] We investigate in detail the nonlinear and chaotic dynamics of the Colpitts oscillator. We show that we can control the dynamics of the oscillator by either inductors, capacitors or resistors in the emitter or collector network. We find the bifurcation diagram and the Lyapunov exponent of the oscillator and investigate them. We also find bifurcation diagram in 2D space when two parameters from the mentioned parameters are variables. The 2D diagram shows the nonlinear behaviour of the system more clearly. (author)