Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control

This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference operator.This is the first study to explore a three-dimensional fractional-order discrete chaotic system without equilibrium.Through phase portrait,bifurcation diagrams,and largest Lyapunov exponents,it is shown that the proposed fractional-order discrete system exhibits a range of different dynamical behaviors.Also,different tests are used to confirm the existence of chaos,such as 0-1 test and C0 complexity.In addition,the quantification of the level of chaos in the new fractional-order discrete system is measured by the approximate entropy technique.Furthermore,based on the fractional linearization method,a one-dimensional controller to stabilize the new system is proposed.Numerical results are presented to validate the findings of the paper.

Theory and Applications of Discontinuous State Feedback Generating Chaos for Linear Systems

We investigate a kind of chaos generating technique on a type of n-dimensional linear differential systems by adding feedback control items under a discontinuous state. This method is checked with some examples of numeric simulation. A constructive theorem is proposed for generalized synchronization related to the above chaotic system.

Chaos block cipher for wireless sensor network

New block cipher algorithm in single byte for wireless sensor network with excellence of many cipher algorithms is studied. The child keys are generated through the developed discrete Logistic mapping, and the Feistel encrypting function with discrete chaos operation is constructed. The single byte block is encrypted and decrypted through one turn permutation, being divided into two semi-byte, quadri- Feistel structural operation, and one turn permutation again. The amount of keys may be variable with the turns of Feistel structural operation. The random and security of the child key was proven, and the experiment for the block cipher in wireless sensor network was completed. The result indicates that the algorithm is more secure and the chaos block cipher in single byte is feasible for wireless sensor network.

Stabilization and Synchronization of Discrete-time Fractional Chaotic Systems with Non-identical Dimensions

This paper investigates the stabilization and synchronization of two fractional chaotic maps proposed recently,namely the 2D fractional Hénon map and the 3D fractional generalized Hénon map.We show that although these maps have non–identical dimensions,their synchronization is still possible.The proposed controllers are evaluated experimentally in the case of non–identical orders or time–varying orders.Numerical methods are used to illustrate the results.

A novel multi-stable sinusoidal chaotic map with spectacular behaviors

Chaotic behavior can be observed in continuous and discrete-time systems.This behavior can appear in one-dimensional nonlinear maps;however,having at least three state variables in flows is necessary.Due to the lower mathematical complexity and computational cost of maps,lots of research has been conducted based on them.This paper aims to present a novel one-dimensional trigonometric chaotic map that is multi-stable and can act attractively.The proposed chaotic map is first analyzed using a single sinusoidal function;then,its abilities are expanded to a map with a combination of two sinusoidal functions.The stability conditions of both maps are investigated,and their different behaviors are validated through time series,state space,and cobweb diagrams.Eventually,the influence of parameter variations on the maps’outputs is examined by one-dimensional and two-dimensional bifurcation diagrams and Lyapunov exponent spectra.Besides,the diversity of outputs with varying initial conditions reveals this map’s multi-stability.The newly designed chaotic map can be employed in encryption applications.

The Dynamics and Control of the Fractional Forms of Some Rational Chaotic Maps

This paper proposes three fractional discrete chaotic systems based on the Rulkov,Chang,and Zeraoulia–Sprott rational maps.The dynamics of the proposed maps are investigated by means of phase plots and bifurcations diagrams.Adaptive stabilization schemes are proposed for each of the three maps and the convergence of the states is established by using the Lyapunov method.Furthermore,a combination synchronization scheme is proposed whereby a combination of the fractional Rulkov and Chang maps is synchronized to the fractional Zeraoulia-Sprott map.Numerical results are used to confirm the findings of the paper.