The first observation of a synchronization phenomenon in physics is attributed to C. Huygens (1673) during his experiments for developing improved pendulum clocks (Huygens, 1673). Two clocks hanging on the same beam of his room were found to oscillate with exactly the same frequency and opposite phase due to the (weak) coupling in terms of the almost imperceptible oscillations of the beam gener...

its variables can still be interpreted in terms of physiological variables, since they have been derived from the physiological variables of the Hodgkin–Huxley model. The other way in which Fitzhugh derived these equations was by introducing one additional parameter in the original van der Pol oscillator equations which modifies them so that they have the qualitative features which Bonhoeffer h...

A mathematical model describing the Hering-Breuer reflexes in mechanically ventilated cats is developed. There is good agreement between the properties of the model and experimental studies performed over a wide range of frequencies and volumes of the mechanical ventilator. There is a correspondence between the model and a periodically forced nonlinear oscillator, similar to the van der Pol equ...

In this work a new approach to stability analysis is applied to nonlinear oscillators. Based on the use of local metrics properties of curvature and torsion resulting from Differential Geometry and while considering trajectory curves as plane or space curves, these properties directly provide their slow manifold analytical equation and its stable and unstable parts. Van der Pol and Colpitts mod...

In this paper we apply the homotopy analysis method (HAM) to study the van der Pol equation with a linear delayed feedback. The paper focuses on the calculation of periodic solutions and associated bifurcations, Hopf, double Hopf, Neimark-Sacker, etc. In particular we discuss the behavior of the systems in the neighborhoods of double Hopf points. We demonstrate the applicability of HAM to the a...