A new color image encryption technique using DNA computing and Chaos-based substitution box

In many cases, images contain sensitive information and patterns that require secure processing to avoid risk. It can be accessed by unauthorized users who can illegally exploit them to threaten the safety of people’s life and property. Protecting the privacies of the images has quickly become one of the biggest obstacles that prevent further exploration of image data. In this paper, we propose a novel privacy-preserving scheme to protect sensitive information within images. The proposed approach combines deoxyribonucleic acid (DNA) sequencing code, Arnold transformation (AT), and a chaotic dynamical system to construct an initial S-box. Various tests have been conducted to validate the randomness of this newly constructed S-box. These tests include National Institute of Standards and Technology (NIST) analysis, histogram analysis (HA), nonlinearity analysis (NL), strict avalanche criterion (SAC), bit independence criterion (BIC), bit independence criterion strict avalanche criterion (BIC-SAC), bit independence criterion nonlinearity (BIC-NL), equiprobable input/output XOR distribution, and linear approximation probability (LP). The proposed scheme possesses higher security wit NL = 103.75, SAC ≈ 0.5 and LP = 0.1560. Other tests such as BIC-SAC and BIC-NL calculated values are 0.4960 and 112.35, respectively. The results show that the proposed scheme has a strong ability to resist many attacks. Furthermore, the achieved results are compared to existing state-of-the-art methods. The comparison results further demonstrate the effectiveness of the proposed algorithm.

Probability distributions for analog-to-target distances

Some properties of chaotic dynamical systems can be probed through features of recurrences, also called analogs. In practice, analogs are nearest neighbours of the state of a system, taken from a large database called the catalog. Analogs have been used in many atmospheric applications including forecasts, downscaling, predictability estimation, and attribution of extreme events. The distances of the analogs to the target state usually condition the performances of analog applications. These distances can be viewed as random variables, and their probability distributions can be related to the catalog size and properties of the system at stake. A few studies have focused on the first moments of return time statistics for the closest analog, fixing an objective of maximum distance from this analog to the target state. However, for practical use and to reduce estimation variance, applications usually require not just one, but many analogs. In this paper, we evaluate from a theoretical standpoint and with numerical experiments the probability distributions of the K shortest analog-to-target distances. We show that dimensionality plays a role on the size of the catalog needed to find good analogs, and also on the relative means and variances of the K closest analogs. Our results are based on recently developed tools from dynamical systems theory. These findings are illustrated with numerical simulations of well-known chaotic dynamical systems and on 10m-wind reanalysis data in north-west France. Practical applications of our derivations are shown for forecasts of an idealized chaotic dynamical system and for objective-based dimension reduction using the 10m-wind reanalysis data.

A 2-D Discrete Cubic Chaotic Mapping with Symmetry

In the theoretical research of chaotic dynamical system, the different type of bifurcations is a very interesting powerful tool for analyzing the qualitative behavior of chaotic dynamical system; this short paper is devoted to analysis of a simple 2-D symmetry discrete chaotic map with quadratic and cubic nonlinearities. The dynamical behaviors of the map are investigated by mathematical analysis and simulated numerically using package of Matlab . We compute numerically the bifurcation diagram and largest Lyapunov exponent and phase portraits. The research results indicate that there are interesting nonlinear physical phenomena in this simple 2-D symmetry discrete cubic map, such as symmetry bifurcation, Hopf bifurcation, symmetry breaking bifurcation and identical symmetric attractors. The important nonlinear physical phenomena obtained in this paper would benefit the study of the cubic chaotic map and the development of the theory of chaotic discrete dynamical systems. En la investigación teórica de los sistemas dinámicos caóticos, los diferentes tipos de bifurcaciones son una herramienta poderosa muy interesante para analizar el comportamiento cualitativo de los sistemas dinámicos caóticos; este breve artículo está dedicado al análisis de un mapa caótico discreto de simetría bidimensional simple con no linealidades cuadráticas y cúbicas. Los comportamientos dinámicos del mapa se investigan mediante análisis matemático y se simulan numéricamente utilizando el paquete de Matlab . Calculamos numéricamente el diagrama de bifurcación y el mayor exponente de Lyapunov y los retratos de fase. Los resultados de la investigación indican que existen interesantes fenómenos físicos no lineales en este sencillo mapa cúbico discreto de simetría 2-D, como la bifurcación de simetría, la bifurcación de Hopf, la bifurcación de ruptura de simetría y los atractores simétricos idénticos. Los importantes fenómenos físicos no lineales obtenidos en este trabajo beneficiarían el estudio del mapa cúbico caótico y el desarrollo de la teoría de los sistemas dinámicos discretos caóticos.

Parameter estimation for a chaotic dynamical system with partial observations

Parameter estimation in chaotic dynamical systems is an important and practical issue. Nevertheless, the high-dimensionality and the sensitive dependence on initial conditions typically makes the problem difficult to solve. In this paper, we propose an innovative parameter estimation approach, utilizing numerical differentiation for observation data preprocessing. Given plenty of noisy observations on a portion of dependent variables, numerical differentiation allows them and their derivatives to be accurately approximated. Substituting those approximations into the original system can effectively simplify the parameter estimation problem. As an example, we consider parameter estimation in the well-known Lorenz model given partial noisy observations. According to the Lorenz equations, the estimated parameters can be simply given by least squares regression using the approximated functions provided by data preprocessing. Numerical examples show the effectiveness and accuracy of our method. We also prove the uniqueness and stability of the solution.

Hurricane dynamics and rapid intensification via dynamical systems indicators

<p>Although the lifecycle of hurricanes is well understood, it is a struggle to represent their dynamics in numerical models, under both present and future climates. We consider the atmospheric circulation as a chaotic dynamical system, and show that the formation of a hurricane corresponds to a reduction of the phase space of the atmospheric dynamics to a low-dimensional state. This behavior is typical of Bose-Einstein condensates. These are states of the matter where all particles have the same dynamical properties. For hurricanes, this corresponds to a "rotational mode" around the eye of the cyclone, with all air parcels effectively behaving as spins oriented in a single direction. This finding paves the way for new parametrisations when simulating hurricanes in numerical climate models.</p>

Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium Points

This paper starts with a review of three-dimensional chaotic dynamical systems equipped with special curves of balance points. We also propose the mathematical model of a new three-dimensional chaotic system equipped with a closed butterfly-like curve of balance points. By performing a bifurcation study of the new system, we analyze intrinsic properties such as chaoticity, multi-stability, and transient chaos. Finally, we carry out a realization of the new multi-stable chaotic model using Field-Programmable Gate Array (FPGA).

New Chaotic Oscillator Derived from Class C Single Transistor-Based Amplifier

This paper describes a new autonomous deterministic chaotic dynamical system having a single unstable saddle-spiral fixed point. A mathematical model originates in the fundamental structure of the class C amplifier. Evolution of robust strange attractors is conditioned by a bilateral nature of bipolar transistor with local polynomial or piecewise linear feedforward transconductance and high frequency of operation. Numerical analysis is supported by experimental verification and both results prove that chaos is neither a numerical artifact nor a long transient behaviour. Also, good accordance between theory and measurement has been observed.