Abstract In this article, we present a microcontroller implementation of the synchronization of two Van der Pol oscillators submitted to disturbances of the pulse-like type. Three coupling schemes are used: the classical linear proportional coupling, a power order coupling and an adaptive coupling. After obtaining the coupling coefficients for synchronization through numerical simulation, the microcontroller implementation is carried out using simulation based on Euler algorithm. Agreement is found between both simulation strategies.

Microcontroller Control/Synchronization of the Dynamics of Van der Pol Oscillators Submitted to Disturbances

A circuit employing resistances, capacitors, operational amplifiers, and diodes in antiparallel as nonlinear elements is analytically, numerically, and experimentally investigated in this chapter. The mathematical model describing the circuit is a three-dimensional autonomous system with a nonlinear term in the form of a hyperbolic sine function. By analyzing the stability of the equilibrium points, the existence of Hopf bifurcation is established. For a suitable choice of the parameters, the circuit displays single- and double-scroll chaotic attractors. The circuit can generate period-doubling bifurcations, symmetry breaking and recovering bifurcations, antimonotonicity, bistabe chaotic attrators, and periodic and chaotic bubbles attractors. Finally, the chaotic attractors generated in the circuit are experimentally confirmed via an electronic realization of the circuit. A good qualitative agreement is illustrated between the numerical and the experimental results.

Analytical, Numerical and Experimental Analysis of an RC Autonomous Circuit With Diodes in Antiparallel

In this paper complete synchronization of diffusively coupled oscillators is considered. We present the results of both, theoretical and experimental investigations of synchronization between two, three and four almost identical oscillators. The method of linear difference signal has been applied. The corresponding differential equations have been integrated analytically and the synchronization threshold has been found. Hardware experiments have been performed and the measured synchronization error of less than 1% has been determined. Good agreement is found between theoretical and experimental results.

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Synchronization of Diffusively Coupled Oscillators: Theory and Experiment

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Synchronization of Diffusively Coupled Oscillators: Theory and Experiment