A time-varying hyperchaotic system and its realization in circuit

Abstract

A hyperchaotic system is often used to generate secure keys or carrier wave for secure communication and the realistic hyperchaotic circuit often is made of capacitor, nonlinear resistor unit and induction coil. Parameters are often fixed in these hyperchaotic circuits and the hyperchaotic property of the system can be estimated by using a scheme of synchronization and time series analysis. In this paper, a time-varying hyperchaotic system is proposed by introducing changeable electric power source into the circuit; the changeable electric power source is combined with induction coil or capacitor in series to generate changeable output signals to excite the system. The diagrams of improved circuit are illustrated and critical parameters in experimental circuits are presented; the Lyapunov exponent spectrum vs. external applied electric power source is calculated. It is confirmed that the improved circuit always holds two positive Lyapunov exponents when the external electric power source works, and the chaotic attractors are much too different from the original one; thus, a more changeable hyperchaotic system is constructed in experiment.

Complex dynamics in a 5-D hyper-chaotic attractor with four-wing, one equilibrium and multiple chaotic attractors

“…Furthermore, time series analysis is often used to measure the dynamical properties of the system. Also, it is important to detect chaos and visualizing the attraction of strange attractors by using nonlinear time series analysis [40,41].…”

Hyperchaos and bifurcations in a driven Van der Pol–Duffing oscillator circuit

“…Electronic circuits exhibiting chaotic behaviour have attracted wide attention because they provide excellent platform for practical implementation of chaotic oscillators (See for example Ref. [5,19,13,24,28,8,2,25,39,35,7,11,23,10,9,30,38] and references therein). Among the several chaotic circuits, the Van der-Pol Duffing oscillator is a very prominent and important classical model circuit that has been extensively studied in the context of several specific problems ranging from global bifurcation structures, control and synchronization (see for example Ref.…”

“…All of the above Van der-Pol Duffing oscillator circuit models deal with self-oscillatory (i. e. autonomous) systems. In this paper, we investigate the dynamics of a nonautonomous unified Van der-Pol Duffing oscillator (UVDP) circuit by introducing a changeable electrical power source (acting as subject to a periodic driving force) [23]. We examine the combined effects of the series and parallel resistances as shown in Figure 1, as well as the periodic driving.…”

Chaos bursting synchronization of mismatched Hindmarsh–Rose systems via a single adaptive feedback controller

“…In the past few years, synchronization of chaotic systems has been extensively studied due to its potential applications in many different areas including secure communication, chemical, and optics and so on [1][2][3]. Since the seminal work of Pecora and Carroll [4], chaos synchronization has received a great deal of interest.…”