Analog circuit implementation and synchronization of a system consisting of a van der Pol oscillator linearly coupled to a Duffing oscillator

Chaos in a System with an Absolute Nonlinearity and Chaos Synchronization

“…Also, most parameters values are characterized by uncertainties related to the modeling errors or experimental conditions (temperature, external electric and magnetic fields, etc.) that can destroy or even break the synchronization [43][44][45]. Therefore, it is essential to consider the synchronization problem of chaotic systems in the presence of unknown system parameters.…”

Secured Transmission of ECG Signals: Numerical and Electronic Simulations

“…Some authors concentrated on designing different oscillators for chaos generation. For example, chaotic behaviours of Duffing, Chua, Colpitts and Van der Pol oscillators [4][5][6][7][8][9], just to name a few, have been studied.…”

“…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.…”

Experiment on Bifurcation and Chaos in Coupled Anisochronous Self-Excited Systems: Case of Two Coupled van der Pol-Duffing Oscillators

“…In contrast to numerical computation, there is no need to wait for long transient times when performing an analog computation. This may serve to explain the increasing interest devoted to this type of implementation for the analysis of complex nonlinear systems [25][26][27]. The aim of this section is to design and implement an appropriate analog circuit/simulator for the analysis of the model defined by the set of (1a) and (1b) in order to verify and complement the theoretical results obtained previously.…”

“…The integrators are built by using operational amplifiers (TL084CN) with feedback capacitors while summations are obtained using operational amplifiers with feedback resistors and input resistors. Adopting an appropriate time scaling [25][26][27], the simulator outputs can directly be displayed on an oscilloscope by connecting the voltages to the input and input. For the oscillator (resp., ) the phase portraits are obtained by feeding the output of 1 (resp., 5 ) to the input and that of 1 (resp., 5 ) to the input.…”