Adaptive backstepping control and synchronization of a modified and chaotic Van der Pol-Duffing oscillator

Abstract

In this paper, we propose a backstepping approach for the synchronization and control of modified Van-der Pol Duffing oscillator circuits. The method is such that one controller function that depends essentially on available circuit parameters that is sufficient to drive the two coupled circuits to a synchronized state as well achieve the global stabilization of the system to its regular dynamics. Numerical simulations are given to demonstrate the effectiveness of the technique.

Secured Transmission of ECG Signals: Numerical and Electronic Simulations

“…A second group of authors was preoccupied by synchronization of chaotic oscillators involved in the emission and reception parts, using a variety of techniques [1][2][3][4][10][11][12][13][14][15][16]. Some of these had secured communications as one of the applications.…”

Master‐Slave Synchronization of Chaotic Φ6 Duffing Oscillators by Linear State Error Feedback Control

“…As is well known, some models for damped and driven oscillators, such as sti ening springs, beam bulking, and superconducting Josephson parametric ampli ers, can be described as Φ 6 Du ng oscillators which have been widely used in mechanical and electrical systems [1,[9][10][11][32][33][34][35][36]. With proper parameters, Du ng oscillators have exhibited chaotic behaviors.…”

“…For chaotic Φ 6 Du ng oscillators, Njah [10,11] used the active control to achieve master-slave synchronization, in which the active control removed all nonlinear terms of the error system. For chaotic Φ 4 Du ng oscillators which is the special case of Φ 6 Du ng oscillators, synchronization criteria were derived by the active control in [32][33][34]37] and [35] in which the linear error system and synchronization criteria were derived. It should be pointed out that chaotic Φ 6 Du ng oscillators are nonlinear systems in which the nonlinear terms play a key role in the generation of chaotic attractors.…”

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

“…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. [19,13,11,10,9,41]).…”