This paper shall discuss the design of a Chaos based symmetric key cryptosystem. The structure of two contemporary symmetric key encryption schemes using the Logistic map is discussed and their performance is evaluated based on a battery of tests and some qualitative measures. It is deduced that one scheme performs far better than the other. It is then experimentally shown that the performance ...

A numerical method for solving the fractional-order logistic differential equation with two different delays FOLE is considered. The fractional derivative is described in the Caputo sense. The proposed method is based upon Chebyshev approximations. The properties of Chebyshev polynomials are utilized to reduce FOLE to a system of algebraic equations. Special attention is given to study the conv...

The recently derived nonlocal quantum kinetic equation for dense interacting Fermi systems combines time derivatives with finite time stepping known from the logistic mapping. This continuous delay differential equation is a consequence of the microscopic delay time representing the dynamics of the deterministic chaotic system. The responsible delay time is explicitly calculated and discussed f...

Abstract : A route to chaos is studied in 3-dimensional maps of logistic type. Mechanisms of period doubling for invariant closed curves (ICC) are found for specific 3-dimensional maps. These bifurcations cannot be observed for ICC in the 2-dimensional case. When the parameter of the system is modified, localized oscillations occur on the ICC that give rise to weakly chaotic rings, then to chao...

We discuss several bifurcation phenomena that occur in the quasiperiodically driven logistic map. This system can have strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors; on SNAs the dynamics is aperiodic, but the largest Lyapunov exponent is nonpositive. There are a number of different transitions that occur here, from periodic attractors to SNAs, from SNAs to c...

We present an improved Markov chain Monte Carlo (MCMC) algorithm for posterior computation in chaotic dynamical systems. Recent Bayesian approaches to estimate the parameters of chaotic maps have used the Gibbs sampler which exhibits slow convergence due to high posterior correlations. Using the extended Kalman filter to compute the likelihood function by integrating out all unknown system stat...

This paper proposes three different chaotic encryption methods using 1-D chaotic map known as Logistic map named as Logistic, NLFSR and Modified NLFSR according to the name of chaotic map and non-linear function involved in the scheme. The designed schemes have been crypt analyzed for five different methods for testing its strength. Cryptanalysis has been performed for various texts using vario...

A novel method to encrypt audio(sound) stream of data by applying chaos is discussed. A pair of one-dimensional logistic maps is used for generating a chaotic sequence. The routine tests of encryption are performed and the results are observed. The proposed scheme is then implemented in real time on a mobile phone and the robustness of the idea is established. Index Terms — chaotic System, ciph...

Owing to their rich dynamical structures, chaotic systems show great potential for the design and employment of chaotic communication devices. The basic idea is that the underlying attractors and repellors of the chaotic system can be used as natural guides for information through suitable intervention in its dynamics (see e.g. Farmer [1], Carroll [2] and Hayes [3] and references therein). Coup...

By introducing Colpitts oscillator as a chaotic system, this paper deals with back-stepping control method and investigates the restrictions and problems of the controller where non-existence of a suitable response in the presence of uncertainty is the most important problem to note. In this paper, the back-stepping sliding mode method is introduced as a robust method for controlling nonlinear ...