In this work we study a system of three van der Pol oscillators, x, y and w, coupled as follows:
Here the x and y oscillators are identical, and are not directly coupled to each other, but rather are coupled via the w oscillator. We investigate the existence of the in-phase mode x = y for ε ≪ 1. To this end we use the two variable expansion perturbation method (also known as multiple scales) to obtain a slow flow, which we then analyze using the software products MACSYMA and AUTO. Our motivation for studying this system comes from the presence of circadian rhythms in the chemistry of the eyes. We model the circadian oscillator in each eye as a van der Pol oscillator (x and y). Although there is no direct connection between the two eyes, they are both connected to the brain, especially to the pineal gland, which is here represented by a third van der Pol oscillator (w).
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