This paper discusses the synchronization of two identical canard-generating oscillators. First, we investigate a canard explosion generated in a system containing a Bonhoeffer-van der Pol (BVP) oscillator using the actual parameter values obtained experimentally. We find that it is possible to numerically observe a canard explosion using this dynamic oscillator. Second, we analyze the complete and in-phase synchronizations of identical canard-generating coupled oscillators via experimental and numerical methods. However, we experimentally determine that a small decrease in the coupling strength of the system induces the collapse of the complete synchronization and the occurrence of a complex synchronization; this finding could not be explained considering four-dimensional autonomous coupled BVP oscillators in our numerical work. To numerically investigate the experimental results, we construct a model containing coupled BVP oscillators that are subjected to two weak periodic perturbations having the same frequency. Further, we find that this model can efficiently numerically reproduce experimentally observed synchronization.

This report presents experimental measurements of mixed-mode oscillations (MMOs) generated by a weakly driven four-segment piecewise linear Bonhoeffer-van der Pol (BVP) oscillator. Such a roughly approximated simple piecewise linear circuit can generate MMOs and mixed-mode oscillation-incrementing bifurcations (MMOIBs). The laboratory experiments well agree with numerical results. We experimentally and numerically observe time series and Lorenz plots of MMOs generated by successive and nonsuccessive MMOIBs.

In this paper, we consider synchronization phenomena in coupled systems of piecewise constant oscillators. Both in-phase and anti-phase synchronization phenomena are observed in the oscillators, which are coupled by a voltage controlled current source (VCCS) with Signum-like characteristic. On the other hand, their co-existence is observed in the oscillators coupled by a VCCS with hysteresis characteristic. We analyze the stability of the synchronization phenomena in the coupled systems by using a fast calculation algorithm for the rigorous solutions. And we clarify the parameter regions of in-phase and anti-phase synchronization by deriving correlation coefficients. We suggest that the synchronization phenomena of the proposed systems qualitatively correspond to one of van der Pol oscillators coupled by passive elements. Some theoretical results are verified in the experimental circuits.

In this brief, a chaotic Jerk system is presented. This was obtained by converting the Van der Pol architecture into a third order differential equation, and, after the state-space representation was obtained, adding one innovation term and modifying some proportional parameters. Using Lyapunov exponents, Poincare maps, Fourier spectrum analysis and numerical experiments, we confirm the chaotic nature of the proposed Jerk system. Experimental results are also included.

The orbital portrait of quasi-periodic oscillation shows transition like change with the amplitude of external force in periodically forced van der Pol oscillator. This phenomenon originates from frequency pulling between self-sustained and periodic external oscillations induced by the frequency shift of former. We estimate this shift and succeed in deriving the transition points at which the portrait changes.