Bidirectional Synchronization of Two Identical Jerk Oscillators with Memristor

In this paper, the case of introducing memristor as a coupling component when synchronizing two identical simple chaotic oscillator (3-D Jerk equations) were observed. Also, the numerical simulation of the phase portraits are in good agreement with the MultiSIM and experimental simulations. Due to the complex chaotic dynamics of this oscillator, the realization of the electronic circuit involving two identical Jerk oscillator with memristor as coupling component were synchronized via bidirectional coupling and further applied to secure communication

Synchronization Limits of Chaotic Circuits

Through system modeling with electronic circuits, two circuits were constructed that exhibit chaos over a wide ranges of initial conditions. The two circuits were one that modeled an algebraically simple “jerk” function and a resistor-inductor-diode (RLD) circuit where the diode was reverse-biased on the positive voltage cycle of the alternating current source. Using simulation data from other experiments, the waveforms, bifurcation plots, and phase space plots of the concrete circuit were verified. Identical circuits were then built containing variable components and coupled to their original, matching circuits. The variable components were used to observe a wide range of conditions to establish the desynchronization parameters and the range of synchronization

A THREE FRACTIONAL ORDER JERK EQUATION WITH ANTI PERIODIC CONDITIONS

We study a new Jerk equation involving three fractional derivatives and anti periodic conditions. By Banach contraction principle, we present an existence and uniqueness result for the considered problem. Utilizing Krasnoselskii fixed point theorem we prove another existence result governing at least one solution. We provide an illustrative example to claim our established results. At the end, an approximation for Caputo derivative is proposed and some chaotic behaviours are discussed by means of the Runge Kutta 4th order method

Chaotic attractors based on unstable dissipative systems via third-order differential equation

"In this paper, we present an approach how to yield 1D, 2D and 3D-grid multi-scroll chaotic systems in R3 based on unstable dissipative systems via third-order differential equation. This class of systems is constructed by a switching control law(SCL) changing the equilibrium point of an unstable dissipative system. The switching control law that governs the position of the equilibrium point varies according to the number of scrolls displayed in the attractor.

A family of hyperchaotic multi-scroll attractors in Rn

Investigació

Hopf bifurcation, antimonotonicity and amplitude controls in the chaotic Toda jerk oscillator: analysis, circuit realization and combination synchronization in its fractional-order form

In this paper, an autonomous Toda jerk oscillator is proposed and analysed. The autonomous Toda jerk oscillator is obtained by converting an autonomous two-dimensional Toda oscillator with an exponential nonlinear term to a jerk oscillator. The existence of Hopf bifurcation is established during the stability analysis of the unique equilibrium point. For a suitable choice of the parameters, the proposed autonomous Toda jerk oscillator can generate antimonotonicity, periodic oscillations, chaotic oscillations and bubbles. By introducing two additional parameters in the proposed autonomous Toda jerk oscillator, it is possible to control partially or totally the amplitude of its signals. In addition, electronic circuit realization of the proposed Toda jerk oscillator is carried out to confirm results found during numerical simulations. The commensurate fractional-order version of the proposed autonomous chaotic Toda jerk oscillator is studied using the stability theorem of fractional-order oscillators and numerical simulations. It is found that periodic oscillations and chaos exist in the fractional-order form of the proposed Toda jerk oscillator with order less than three. Finally, combination synchronization of two fractional-order proposed autonomous chaotic Toda jerk oscillators with another fractional-order proposed autonomous chaotic Toda jerk oscillator is analysed using the nonlinear feedback control method

Temperature as a Chaotic Circuit Bifurcation Parameter

The number of researches aimed at understanding the chaotic behavior of nonlinear dynamical systems has grown considerably in recent years. The development of electronic circuits that exhibit this type of behavior has been the interest of numerous works in the literature. Among the possible sets of nonlinear systems, the simplest in which one can observe bifurcation phenomena and chaotic behavior, followed by well– controlled experiments, are nonlinear electronic circuits. One of the most widely used tools for analysis and evaluation of chaotic behavior is known as the bifurcation diagram. Generally, in the analysis of these circuits, parameters such as voltage, current and frequency are used to verify their respective behaviors. Variable values of passive components such as resistors and capacitors are also widely used. The temperature has also been used as a bifurcation parameter in resistor, diode and inductor (RLD) circuits. However, there is little attention from the scientific community on temperature as a bifurcation parameter for electronic circuits using operational amplifiers such as the chaotic Jerk circuit. In this sense, this project aims to implement a chaotic Jerk circuit, composed of operational amplifiers, resistors and capacitors, and subject it to different temperature levels, using this variable as an analysis parameter. Thus, at the end of this work it was possible to verify that the temperature variation directly influences the behavior of the investigated system, thus reaching the final objective of the project, presenting that the temperature can be a bifurcation parameter for a chaotic Jerk circuit