Dynamics of three coupled van der Pol oscillators with application to circadian rhythms |
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| Institution: | 1. Laboratory of Electronics and Signal Processing, Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 067, Dschang, Cameroon;2. Instituto de Física Teórica, UNESP, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271,Bloco II, Barra Funda, São Paulo\n01140-070, Brazil;1. School of Computer Science & Technology, Anhui University of Technology, Ma’anshan 243032, PR China;2. Research Institute of Information Technology, Anhui University of Technology, Ma''anshan 243000, PR China;3. College of Mathematics and Systems Science, Shandong University of Science & Technology, Qingdao 266590, PR China |
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| Abstract: | In this work we study a system of three van der Pol oscillators. Two of the oscillators are identical, and are not directly coupled to each other, but rather are coupled via the third oscillator. We investigate the existence of the in-phase mode in which the two identical oscillators have the same behavior. 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 computer algebra system MACSYMA and the numerical bifurcation software 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. 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. |
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