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

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

A simple multi-stable chaotic jerk system with two saddle-foci equilibrium points: analysis, synchronization via backstepping technique and MultiSim circuit design

This paper announces a new three-dimensional chaotic jerk system with two saddle-focus equilibrium points and gives a dynamic analysis of the properties of the jerk system such as Lyapunov exponents, phase portraits, Kaplan-Yorke dimension and equilibrium points. By modifying the Genesio-Tesi jerk dynamics (1992), a new jerk system is derived in this research study. The new jerk model is equipped with multistability and dissipative chaos with two saddle-foci equilibrium points. By invoking backstepping technique, new results for synchronizing chaos between the proposed jerk models are successfully yielded. MultiSim software is used to implement a circuit model for the new jerk dynamics. A good qualitative agreement has been shown between the MATLAB simulations of the theoretical chaotic jerk model and the MultiSIM result

ASB-CS: Adaptive sparse basis compressive sensing model and its application to medical image encryption

Recent advances in intelligent wearable devices have brought tremendous chances for the development of healthcare monitoring system. However, the data collected by various sensors in it are user-privacy-related information. Once the individuals’ privacy is subjected to attacks, it can potentially cause serious hazards. For this reason, a feasible solution built upon the compression-encryption architecture is proposed. In this scheme, we design an Adaptive Sparse Basis Compressive Sensing (ASB-CS) model by leveraging Singular Value Decomposition (SVD) manipulation, while performing a rigorous proof of its effectiveness. Additionally, incorporating the Parametric Deformed Exponential Rectified Linear Unit (PDE-ReLU) memristor, a new fractional-order Hopfield neural network model is introduced as a pseudo-random number generator for the proposed cryptosystem, which has demonstrated superior properties in many aspects, such as hyperchaotic dynamics and multistability. To be specific, a plain medical image is subjected to the ASB-CS model and bidirectional diffusion manipulation under the guidance of the key-controlled cipher flows to yield the corresponding cipher image without visual semantic features. Ultimately, the simulation results and analysis demonstrate that the proposed scheme is capable of withstanding multiple security attacks and possesses balanced performance in terms of compressibility and robustness

A New Class of Two-dimensional Chaotic Maps with Closed Curve Fixed Points

This is the author accepted manuscript. The final version is available from World Scientific Publishing via the DOI in this recordThis paper constructs a new class of two-dimensional maps with closed curve fixed points. Firstly, the mathematical model of these maps is formulated by introducing a nonlinear function. Different types of fixed points which form a closed curve are shown by choosing proper parameters of the nonlinear function. The stabilities of these fixed points are studied to show that these fixed points are all non-hyperbolic. Then a computer search program is employed to explore the chaotic attractors in these maps, and several simple maps whose fixed points form different shapes of closed curves are presented. Complex dynamical behaviours of these maps are investigated by using the phase-basin portrait, Lyapunov exponents, and bifurcation diagrams.National Natural Science Foundation of ChinaNatural Science Foundation of Jiangsu Province of China5th 333 High-level Personnel Training Project of Jiangsu Province of ChinaExcellent Scientific and Technological Innovation Team of Jiangsu UniversityJiangsu Key Laboratory for Big Data of Psychology and Cognitive Scienc

Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion

In this tutorial, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky--Dolghansky and Rabinovich systems, to demonstrate the analysis of self-excited and hidden attractors and their characteristics. We applied the fishing principle to demonstrate the existence of a homoclinic orbit, proved the dissipativity and completeness of the system, and found absorbing and positively invariant sets. We have shown that this system has a self-excited attractor and a hidden attractor for certain parameters. The upper estimates of the Lyapunov dimension of self-excited and hidden attractors were obtained analytically.Comment: submitted to EP

Coexisting Three-Scroll and Four-Scroll Chaotic Attractors in a Fractional-Order System by a Three-Scroll Integer-Order Memristive Chaotic System and Chaos Control

Based on the integer-order memristive system that can generate two-scroll, three-scroll, and four-scroll chaotic attractors, in this paper, we found other phenomena that two kinds of three-scroll chaotic attractors coexist in this system with different initial conditions. Furthermore, we proposed a coexisting fractional-order system based on the three-scroll chaotic attractors system, in which the three-scroll or four-scroll chaotic attractors emerged with different fractional-orders q. Meanwhile, with fractional-order q=0.965 and different initial conditions, coexistence of two kinds of three-scroll and four-scroll chaotic attractors is found simultaneously. Finally, we discussed controlling chaos for the fractional-order memristive chaotic system

Low-Cost Inventions and Patents

Inventions have led to the technological advances of mankind. There are inventions of all kinds, some of which have lasted hundreds of years or even longer. Low-cost technologies are expected to be easy to build, have little or no energy consumption, and be easy to maintain and operate. The use of sustainable technologies is essential in order to move towards a greater global coverage of technology, and therefore to improve human quality of life. Low-cost products always respond to a specific need, even if no in-depth analysis of the situation or possible solutions has been carried out. It is a consensus in all industrialized countries that patents have a decisive influence on the organization of the economy, as they are a key element in promoting technological innovation. Patents must aim to promote the technological development of countries, starting from their industrial situations

18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems: Proceedings

Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.:Welcome Address ........................ Page I Table of Contents ........................ Page III Symposium Committees .............. Page IV Special Thanks ............................. Page V Conference program (incl. page numbers of papers) ................... Page VI Conference papers Invited talks ................................ Page 1 Regular Papers ........................... Page 14 Wednesday, May 26th, 2010 ......... Page 15 Thursday, May 27th, 2010 .......... Page 110 Friday, May 28th, 2010 ............... Page 210 Author index ............................... Page XII