Christos Volos

Constructing a Novel No-Equilibrium Chaotic System

This paper introduces a new no-equilibrium chaotic system that is constructed by adding a tiny perturbation to a simple chaotic flow having a line equilibrium. The dynamics of the proposed system are investigated through Lyapunov exponents, bifurcation diagram, Poincare map and period-doubling route to chaos. A circuit realization is also represented. Moreover, two other new chaotic systems without equilibria are also proposed by applying the presented methodology.

A Novel No-Equilibrium Chaotic System with Multiwing Butterfly Attractors

Discovering unknown features of no-equilibrium systems with hidden strange attractors is an attractive research topic. This paper presents a novel no-equilibrium chaotic system that is constructed by using a state feedback controller. Interestingly, the new system can exhibit multiwing butterfly attractors. Moreover, a new chaotic system with an infinite number of equilibrium points, which can generate multiscroll attractors, is also proposed by applying the introduced methodology.

A Chaotic System With Equilibria Located on the Rounded Square Loop and Its Circuit Implementation

A new 3-D chaotic system with infinitely many equilibria is proposed in this brief. It is exciting that these equilibrium points are located on a rounded square loop. Dynamical properties and the circuit implementation of the system are studied and reported.

Advances and Applications in Chaotic Systems

This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.

Multi-scroll Chaotic Oscillator Based on a First-Order Delay Differential Equation

After the discovery of the well-known chaotic Lorenz’s system, the study of chaos has received considerable attention due to its promising applications in a variety of fields, ranging from physics, economics, biology to engineering. Moreover, chaotic systems with multiple scrolls can exhibit more rich dynamics than the general chaotic ones with few attractors. This expansion of dynamics leads to multi-scroll chaotic oscillators showing better performance in several chaotic-based applications, such as secure communication, encrypting fingerprint image, controlling motion directions of autonomous mobile robots, or generating pseudo random numbers etc. As a result, investigating new chaotic oscillators with multiple scrolls has been become an attractive research direction of both theoretical and practical interest recently. Although numerous approaches for constructing multi-scroll attractors from conventional three-dimension chaotic systems have been reported intensively, there are few publications regarding the multi-scroll attractors from infinite dimensional time-delay systems. This work presents a new multi-scroll chaotic oscillator and its circuital design. This chaotic system is described by a first-order delay differential equation with piecewise linear function. It is shown through simulations that the proposed system can exhibit odd number of scrolls of chaotic attractors such as three-, five-, seven-, and nine-scroll attractors. In addition, the detailed implementation of the proposed multi-scroll oscillator using the electronic simulation package Multisim is also presented to show the feasibility of the oscillator. The Multisim results of the chaotic oscillator are well agree with the numerical simulation results. It is noting that the new multi-scroll chaotic circuit has been designed with simple common components, like resistors, capacitors, and operational amplifiers.

Analysis, adaptive control and circuit simulation of a novel nonlinear finance system

In the last three decades a growing interest in developing nonlinear dynamical systems for economic models, displaying chaotic behavior has been developed. To this direction, a novel 3-D nonlinear finance chaotic system consisting of two nonlinearities is presented. The dynamical analysis of the proposed system confirms its complex dynamic behavior, which is studied by using well-known simulation tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents and phase portraits. Also, some interesting phenomena related with nonlinear theory are observed, such as route to chaos through a period doubling sequence, antimonotonicity and crisis phenomena. In addition, an interesting scheme of adaptive control of finance systems behavior is presented. Furthermore, the novel nonlinear finance system is emulated by an electronic circuit and its dynamical behavior is studied by using the electronic simulation package Cadence OrCAD in order to confirm the feasibility of the theoretical model.

Is that Really Hidden? The Presence of Complex Fixed-Points in Chaotic Flows with No Equilibria

In this letter we investigate the role of complex fixed-points in finding hidden attractors in chaotic flows with no equilibria. If these attractors could be found by starting the trajectory in the neighborhood of complex fixed-points, maybe it would be better not to call them hidden.

Advances and Applications in Nonlinear Control Systems

The book reports on the latest advances and applications of nonlinear control systems. It consists of 30 contributed chapters by subject experts who are specialized in the various topics addressed in this book. The special chapters have been brought out in the broad areas of nonlinear control systems such as robotics, nonlinear circuits, power systems, memristors, underwater vehicles, chemical processes, observer design, output regulation, backstepping control, sliding mode control, time-delayed control, variables structure control, robust adaptive control, fuzzy logic control, chaos, hyperchaos, jerk systems, hyperjerk systems, chaos control, chaos synchronization, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in nonlinear control systems. This book will serve as a reference book for graduate students and researchers with a basic knowledge of electrical and control systems engineering. The resulting design procedures on the nonlinear control systems are emphasized using MATLAB software

A Chaotic System with Different Families of Hidden Attractors

The presence of hidden attractors in dynamical systems has received considerable attention recently both in theory and applications. A novel three-dimensional autonomous chaotic system with hidden attractors is introduced in this paper. It is exciting that this chaotic system can exhibit two different families of hidden attractors: hidden attractors with an infinite number of equilibrium points and hidden attractors without equilibrium. Dynamical behaviors of such system are discovered through mathematical analysis, numerical simulations and circuit implementation.

Global Chaos Control of a Novel Nine-Term Chaotic System via Sliding Mode Control

Chaotic systems are nonlinear dynamical systems which are very sensitive to even small changes in the initial conditions. The control of chaotic systems is to design state feedback control laws that stabilize the chaotic systems around the unstable equilibrium points. This work derives a general result for the global chaos control of novel chaotic systems using sliding mode control. The main result has been proved using Lyapunov stability theory. Sliding mode control (SMC) is well-known as a robust approach and useful for controller design in systems with parameter uncertainties. Next, a novel nine-term 3-D chaotic system has been proposed in this paper and its properties have been detailed. The Lyapunov exponents of the novel chaotic system are found as \(L_1 = 6.8548, L_2 = 0\) and \(L_3 = -32.8779\) and the Lyapunov dimension of the novel chaotic system is found as \(D_L = 2.2085\). The maximal Lyapunov exponent of the novel chaotic system is \(L_1 = 6.8548\). As an application of the general result derived in this work, a sliding mode controller is derived for the global chaos control of the identical novel chaotic systems. MATLAB simulations have been provided to illustrate the qualitative properties of the novel 3-D chaotic system and the sliding controller results for the stabilizing control developed for the novel 3-D chaotic system.