On distributional chaos in non-autonomous discrete systems

This paper studies distributional chaos in non-autonomous discrete systems generated by given sequences of maps in metric spaces. In the case that the metric space is compact, it is shown that a system is Li-Yorke{\delta}-chaotic if and only if it is distributionally{\delta}'-chaotic in a sequence; and three criteria of distributional {\delta}-chaos are established, which are caused by topologically weak mixing, asymptotic average shadowing property, and some expanding condition, respectively, where {\delta} and {\delta}' are positive constants. In a general case, a criterion of distributional chaos in a sequence induced by a Xiong chaotic set is established.Comment: Chaos, Solitons & Fractals to appear, 25 page

Parrondo's games with chaotic switching

This paper investigates the different effects of chaotic switching on Parrondo's games, as compared to random and periodic switching. The rate of winning of Parrondo's games with chaotic switching depends on coefficient(s) defining the chaotic generator, initial conditions of the chaotic sequence and the proportion of Game A played. Maximum rate of winning can be obtained with all the above mentioned factors properly set, and this occurs when chaotic switching approaches periodic behavior.Comment: 11 pages, 9 figure

A novel approach to security enhancement of chaotic DSSS systems

In this paper, we propose a novel approach to the enhancement of physical layer security for chaotic direct-sequence spread-spectrum (DSSS) communication systems. The main idea behind our proposal is to vary the symbol period according to the behavior of the chaotic spreading sequence. As a result, the symbol period and the spreading sequence vary chaotically at the same time. This simultaneous variation aims at protecting DSSS-based communication systems from the blind estimation attacks in the detection of the symbol period. Discrete-time models for spreading and despreading schemes are presented and analyzed. Multiple access performance of the proposed technique in the presence of additional white Gaussian noise (AWGN) is determined by computer simulations. The increase in security at the physical layer is also evaluated by numerical results. Obtained results show that our proposed technique can protect the system against attacks based on the detection of the symbol period, even if the intruder has full information on the used chaotic sequence.Peer ReviewedPostprint (author's final draft

Cryptanalysis of an Image Encryption Scheme Based on a Compound Chaotic Sequence

Recently, an image encryption scheme based on a compound chaotic sequence was proposed. In this paper, the security of the scheme is studied and the following problems are found: (1) a differential chosen-plaintext attack can break the scheme with only three chosen plain-images; (2) there is a number of weak keys and some equivalent keys for encryption; (3) the scheme is not sensitive to the changes of plain-images; and (4) the compound chaotic sequence does not work as a good random number resource.Comment: 11 pages, 2 figure

Quantitative and qualitative Kac's chaos on the Boltzmann's sphere

We investigate the construction of chaotic probability measures on the Boltzmann's sphere, which is the state space of the stochastic process of a many-particle system undergoing a dynamics preserving energy and momentum. Firstly, based on a version of the local Central Limit Theorem (or Berry-Esseen theorem), we construct a sequence of probabilities that is Kac chaotic and we prove a quantitative rate of convergence. Then, we investigate a stronger notion of chaos, namely entropic chaos introduced in \cite{CCLLV}, and we prove, with quantitative rate, that this same sequence is also entropically chaotic. Furthermore, we investigate more general class of probability measures on the Boltzmann's sphere. Using the HWI inequality we prove that a Kac chaotic probability with bounded Fisher's information is entropically chaotic and we give a quantitative rate. We also link different notions of chaos, proving that Fisher's information chaos, introduced in \cite{HaurayMischler}, is stronger than entropic chaos, which is stronger than Kac's chaos. We give a possible answer to \cite[Open Problem 11]{CCLLV} in the Boltzmann's sphere's framework. Finally, applying our previous results to the recent results on propagation of chaos for the Boltzmann equation \cite{MMchaos}, we prove a quantitative rate for the propagation of entropic chaos for the Boltzmann equation with Maxwellian molecules.Comment: 51 pages, to appear in Ann. Inst. H. Poincar\'e Probab. Sta