Physics

Recent developments in the theory of nonlinear dynamics have paved the way for analyzing signals generated from nonlinear biological systems. This study is aimed at investigating the application of nonlinear analysis in differentiating between patients and healthy persons, as well as in investigating the relation between ergodicity and stationarity in the dynamics of the heart. The nonlinear analysis in this work includes attractor reconstruction, estimation of the correlation dimension, calculation of the largest Lyapunov exponent, the approximate entropy, the sample entropy, and a Poincaré plot. Four groups of electrical cardiograph (ECG) signals have been investigated. Our results, obtained from clinical data, confirm the previous studies; this allows one to distinguish between a healthy group and a group of patients with more confidence than the standard methods for heart rate time series. Furthermore we extended our understanding of heart dynamics using entropies and a Poincaré plot along with the correlation dimension and the largest Lyapunov exponent. We have also obtained the results that stationarity and ergodicity are related to each other in heart dynamics.

By choosing a dynamical system with d different couplings, one can rearrange a system based on the graph with given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a relation between the vertexes. Based on the E 0 transverse projection operator. We addressed synchronization problem of an array of the linearly coupled map lattices of identical discrete time systems.

A simple model for nuclear reactor is proposed. With increasing the fuel concentration, our minimal model shows two successive phases; subcritical and supercritical. In subcritical regime, the neutron population grows with increasing the fuel concentration. In the supercritical state, the Lyapunov exponent is positive implying that the neutron diffusion phenomena are spatiotemporal chaos. In the present paper, the infinite multiplication factor curve is qualitatively reproduced for fuel concentration. We have derived the critical fuel concentration based on the Lyapunov exponents. The basic objective of the work is to improve the prediction of the critical neutron population with respect to the fuel concentration.

This paper studies the stability of the slab reactor with respect to the enrichment. For this purpose, the coupled map lattice theory is applied to the multi-group diffusion equations. Applying mean Lyapunov exponent theory introduced by Shibata [H. Shibata, Physica A 264 (1999) 226] on the model shows that, two successive phases: subcritical and supercritical. In order to compare the performance of the selected method by using the MCNP and ANISN codes the obtained results controlled. The model, in spite of its simplicity in form, shows a greater efficiency in prediction of critical enrichment.

Techniques for stabilizing unstable state in nonlinear dynamical systems using small perturbations fall into three general categories: feedback, non-feedback schemes, and a combination of feedback and non-feedback. However, the general problem of finding conditions for creation or suppression of chaos still remains open. We describe a method for dynamical control of chaos. This method is based on a definition of the hierarchy of solvable chaotic maps with dynamical parameter as a control parameter. In order to study the new mechanism of control of chaotic process, Kolmogorov-Sinai entropy of the chaotic map with dynamical parameter based on discussion the properties of invariant measure have been calculated and confirmed by calculation of Lyapunov exponents. The introduced chaotic maps can be used as dynamical control.

Chaos-based encryption appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an implementation of digital image encryption scheme based on the mixture of chaotic systems is reported. The chaotic cryptography technique used in this paper is a symmetric key cryptography. In this algorithm, a typical coupled map was mixed with a one-dimensional chaotic map and used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail, along with its security analysis and implementation. The experimental results based on mixture of chaotic maps approves the effectiveness of the proposed method and the implementation of the algorithm. This mixture application of chaotic maps shows advantages of large key space and high-level security. The ciphertext generated by this method is the same size as the plaintext and is suitable for practical use in the secure transmission of confidential information over the Internet.

Security of information has become a major issue during the last decades. New algorithms based on chaotic maps were suggested for protection of different types of multimedia data, especially digital images and videos in this period. However, many of them fundamentally were flawed by a lack of robustness and security. For getting higher security and higher complexity, in the current paper, we introduce a new kind of symmetric key block cipher algorithm that is based on tripled chaotic maps. In this algorithm, the utilization of two coupling parameters, as well as the increased complexity of the cryptosystem, make a contribution to the development of cryptosystem with higher security. In order to increase the security of the proposed algorithm, the size of key space and the computational complexity of the coupling parameters should be increased as well. Both the theoretical and experimental results state that the proposed algorithm has many capabilities such as acceptable speed and complexity in the algorithm due to the existence of two coupling parameter and high security. Note that the ciphertext has a flat distribution and has the same size as the plaintext. Therefore, it is suitable for practical use in secure communications. *

Chaotic cryptology has been widely investigated recently. A common feature in the most recent developments of chaotic cryptosystems is the use of a single dynamical rule in the encoding-decoding process. The main objective of this paper is to provide a set of chaotic systems instead of a single one for cryptography. In this paper, we introduce a chaotic cryptosystem based on the symbolic dynamics of random maps with position dependent weighting probabilities. The random maps model is a deterministic dynamical system in a finite phase space with n points. The maps that establish the dynamics of the system are chosen randomly for every point. The essential idea of this paper is that, given two dynamical systems that behave in a certain way, it is possible to combine them (by composing) into a new dynamical system. This dynamically composed system behaves in a completely different way compared to the constituent systems. The proposed scheme exploits the symbolic dynamics of a set of chaotic maps in order to encode the binary information. The performance of the new cryptosystem based on chaotic dynamical systems properties is examined. Both theoretical and experimental results demonstrate that the proposed algorithm using symbolic dynamics achieves the optimal security criteria.

In this letter a new watermarking scheme for color image is proposed based on a family of the pair-coupled maps. Pair-coupled maps are employed to improve the security of watermarked image, and to encrypt the embedding position of the host image. Another map is also used to determine the pixel bit of host image for the watermark embedding. The purpose of this algorithm is to improve the shortcoming of watermarking such as small key space and low security. Due to the sensitivity to the initial conditions of the introduced pair-coupled maps, the security of the scheme is greatly improved.

In recent years, a growing number of cryptosystems based on chaos have been proposed. But most of them encountered many problems such as small key space and weak security. In the present paper, a new kind of chaotic cryptosystem based on Composition of Trigonometric Chaotic Maps is proposed.

The spectral properties of the Perron-Frobenius operator of the one-dimensional maps are studied by using the moment. In this paper we make an investigation into the properties of self-similar measures related to the theory of orthogonal polynomials. Numerical investigation of a particular family of maps shows that the spectrum generates the invariant measure. Analytical considerations generalize the results to a broader class of the maps. Some examples of this method are presented through out the paper.

Stability control in laser is still an emerging field of research. In this paper the dynamics of External cavity semiconductor lasers (ECSLs) is widely studied applying the methods of chaos physics. The stability is analyzed through plotting the Lyapunov exponent spectra, bifurcation diagrams and time series. The results of the study show that the rich nonlinear dynamics of the electric field intensity (| E | 2 ) includes saddle node bifurcations, periodic, quasi periodic, chaotic and regular pulse packages. The issue of finding the conditions for creating stable domains has been studied. By considering the dynamical pumping current system coupled with laser, a method for the creation of the stable domain has been introduced. Usage:

An interesting hierarchy of random number generators is introduced in this paper based on the review of random numbers characteristics and chaotic functions theory. The main objective of this paper is to produce an ergodic dynamical system which can be implemented in random number generators. In order to check the efficacy of pseudo random number generators based on this map, we have carried out certain statistical tests on a series of numbers obtained from the introduced hierarchy. The results of the tests were promising, as the hierarchy passed the tests satisfactorily, and offers a great capability to be employed in a pseudo random number generator.

We give a hierarchy of many-parameter families of maps of the interval [0, 1] with an invariant measure and using the measure, we calculate Kolmogorov-Sinai entropy of these maps analytically. In contrary to the usual one-dimensional maps these maps do not possess period doubling or period-n-tupling cascade bifurcation to chaos, but they have single fixed point attractor at certain region of parameters space, where they bifurcate directly to chaos without having period-n-tupling scenario exactly at certain values of the parameters.

In this paper, a hierarchy of two-dimensional piecewise nonlinear chaotic maps with an invariant measure is introduced. These maps have interesting features such as invariant measure, ergodicity and the possibility of K-S entropy calculation. Then by using significant properties of these chaotic maps such as ergodicity, sensitivity to initial condition and control parameter, one-way computation and random like behavior, we present a new scheme for image encryption. Based on all analysis and experimental results, it can be concluded that, this scheme is efficient, practicable and reliable, with high potential to be adopted for network security and secure communications. Although the two-dimensional piecewise nonlinear chaotic maps presented in this paper aims at image encryption, it is not just limited to this area and can be widely applied in other information security fields.

In recent years, a growing number of discrete chaotic cryptographic algorithms have been proposed. However, most of them encounter some problems such as the lack of robustness and security. In this Letter, we introduce a new image encryption algorithm based on one-dimensional piecewise nonlinear chaotic maps. The system is a measurable dynamical system with an interesting property of being either ergodic or having stable period-one fixed point. They bifurcate from a stable single periodic state to chaotic one and vice versa without having usual period-doubling or period-n-tupling scenario. Also, we present the KS-entropy of this maps with respect to control parameter. This algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security.

We present hierarchy of one and many-parameter families of elliptic chaotic maps of cn and sn types at the interval [0, 1]. It is proved that for small values of k the parameter of the elliptic function, these maps are topologically conjugate to the maps of references , where using this we have been able to obtain the invariant measure of these maps for small k and thereof it is shown that these maps have the same Kolmogorov-Sinai entropy or equivalently Lyapunov characteristic exponent of the maps [1, 2]. As this parameter vanishes, the maps are reduced to the maps presented in above-mentioned reference. Also in contrary to the usual family of one-parameter maps, such as the logistic and tent maps, these maps do not display period doubling or period-n-tupling cascade transition to chaos, but they have single fixed point attractor at certain parameter values where they bifurcate directly to chaos without having period-n-tupling scenario exactly at these values of parameters whose Lyapunov characteristic exponent begin to be positive.

The selection of the potential parameters is a very difficult question because the potentials entering the model are effective potentials. In this Letter, an approach for selecting potential parameters of the Peyrard-Bishop model by mean Lyapunov exponent is presented. Using the theory introduced by Shibata [H. Shibata, Physica A 264 (1999) 226] on the Peyrard-Bishop model shows that, the system is very sensitive to the parameters selection. The obtained results demonstrate that the best range for parameters are where the mean Lyapunov exponent has low values. Furthermore, there is a good correspondence between our results and other reports.