Periodic orbits in glycolytic oscillators: From elliptic orbits to relaxation oscillations
Department of Physics, Jadavpur University, 700032, Kolkata, India
2 S. N. Bose National Centre for Basic Sciences, Salt Lake, 700098, Kolkata, India
Accepted: 19 January 2011
Published online: 28 February 2011
We consider the Sel’kov model of glycolytic oscillator for a quantitative study of the limit cycle oscillations in the system. We identify a region of parameter space where perturbation theory holds and use both Linstedt Poincaré technique and harmonic balance to obtain the shape and frequency of the limit cycle. The agreement with the numerically obtained result is excellent. We also find a different extreme, where the limit cycle is of the relaxation oscillator variety, has a large time period and it is seen that, as a particular parameter in the model is varied, the time period increases indefinitely. We characterize this divergence numerically. A calculational method is devised to capture the divergence approximately.
© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2011