Bifurcation and Chaos in Fractional-Order Systems

This book presents a collection of seven technical papers on fractional-order complex systems, especially chaotic systems with hidden attractors and symmetries, in the research front of the field, which will be beneficial for scientific researchers, graduate students, and technical professionals to study and apply. It is also suitable for teaching lectures and for seminars to use as a reference on related topics

On the Application of PSpice for Localised Cloud Security

The work reported in this thesis commenced with a review of methods for creating random binary sequences for encoding data locally by the client before storing in the Cloud. The first method reviewed investigated evolutionary computing software which generated noise-producing functions from natural noise, a highly-speculative novel idea since noise is stochastic. Nevertheless, a function was created which generated noise to seed chaos oscillators which produced random binary sequences and this research led to a circuit-based one-time pad key chaos encoder for encrypting data. Circuit-based delay chaos oscillators, initialised with sampled electronic noise, were simulated in a linear circuit simulator called PSpice. Many simulation problems were encountered because of the nonlinear nature of chaos but were solved by creating new simulation parts, tools and simulation paradigms. Simulation data from a range of chaos sources was exported and analysed using Lyapunov analysis and identified two sources which produced one-time pad sequences with maximum entropy. This led to an encoding system which generated unlimited, infinitely-long period, unique random one-time pad encryption keys for plaintext data length matching. The keys were studied for maximum entropy and passed a suite of stringent internationally-accepted statistical tests for randomness. A prototype containing two delay chaos sources initialised by electronic noise was produced on a double-sided printed circuit board and produced more than 200 Mbits of OTPs. According to Vladimir Kotelnikov in 1941 and Claude Shannon in 1945, one-time pad sequences are theoretically-perfect and unbreakable, provided specific rules are adhered to. Two other techniques for generating random binary sequences were researched; a new circuit element, memristance was incorporated in a Chua chaos oscillator, and a fractional-order Lorenz chaos system with order less than three. Quantum computing will present many problems to cryptographic system security when existing systems are upgraded in the near future. The only existing encoding system that will resist cryptanalysis by this system is the unconditionally-secure one-time pad encryption

Stable orbits in the proximity of an asteroid: solutions for the Hayabusa 2 mission

This thesis studies the dynamics that arise in the surroundings of a small asteroid with the objective of identifying feasible trajectories for use in the Japanese mission Hayabusa 2. Hayabusa 2, which is expected to be launched at the end of year 2014, will travel to near earth asteroid 1999 JU3 and rendezvous with it. The main purpose of the mission is to collect a sample of the asteroid’s rock and carry it back to the earth for a detailed analysis. The spacecraft, however, will remain close to the asteroid for approximately 1.5 years, and it will perform several other types of scientific observations. All of the operations will be carried out from a controlled hovering position, that is, a fixed point between the earth the asteroid, close to the latter. This study aims at finding orbital strategies, different from hovering, that can enhance the scientific returns of this phase. In particular, orbits passing repeatedly close to the asteroid would provide a wealth of information on the gravitational field, and thus the internal structure, that would not be available through simple hovering. A first part of this work is focused on the circular augmented Hill’s 3–body problem, a formulation similar to the restricted 3-body problem that well describes the asteroidal environment, including solar radiation pressure. In this system we perform a grid search that results in a collection of several periodic orbits. We study a group of these orbits in detail, constructing their whole families with numerical continuation and analyzing their stability properties. The orbit families are also subject to a comparison on the basis of the characteristics most appropriate to Hayabusa 2. The result of this part is the identification of a type of orbit that is most feasible for the Japanese mission. Not treated in the above part are the two other important properties of the dynamical system, that is, the inhomogeneity of the asteroid’s mass and the ellipticity of its orbit around the sun. These are considered in the second part as perturbations, and a linear quadratic regulator (LQR) is set up in order to actively eliminate them. We show that the LQR is capable of stabilizing the periodic orbits against these and other effects, using thrusts attainable, in theory, with electric propulsion. The final part of this thesis addresses the need for trajectories that are stable in the elliptic Hill’s problem without any control. Rather then looking for periodic orbits in this more complex system, we use the results from the circular case to identify non-periodic repetitive trajectories that are nonetheless stable. The result in a map of the space of initial conditions containing a wide group of trajectories that neither impact nor escape from the asteroids for long periods of time. Among these trajectories, some are especially suitable for the purposes and instrument requirements of Hayabusa 2

Entropy in Dynamic Systems

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed

Quantum Chaotic Cryptography : A New Approach

Sejak 1990-an, sistem rawak dinamik digunakan secara meluas untuk mereka bentuk strategi baru bagi menyulitkan maklumat dalam bidang analog dan digital. Kini, banyak kriptosistem yang berasaskan rawak digital dicadangkan dan sebilangan daripada mereka dikriptanalisis. Since 1990s chaotic dynamical systems have been widely used to design new strategies to encrypt information in analog and digital areas. Recently, many digital chaos-based cryptosystems are proposed and a number of them have been cryptanalyzed

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue