Estimating the boundaries of a limit cycle in a 2D dynamical system using renormalization group

Dutta, Ayan ; Das, Debapriya ; Banerjee, Dhruba ; Bhattacharjee, Jayanta K. (2018) Estimating the boundaries of a limit cycle in a 2D dynamical system using renormalization group Communications in Nonlinear Science and Numerical Simulation, 57 . pp. 47-57. ISSN 1007-5704

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Official URL: http://doi.org/10.1016/j.cnsns.2017.06.010

Related URL: http://dx.doi.org/10.1016/j.cnsns.2017.06.010

Abstract

While the plausibility of formation of limit cycle has been a well studied topic in context of the Poincare–Bendixson theorem, studies on estimates in regard to the possible size and shape of the limit cycle seem to be scanty in the literature. In this paper we present a pedagogical study of some aspects of the size of this limit cycle using perturbative renormalization group by doing detailed and explicit calculations upto second order for the Selkov model for glycolytic oscillations. This famous model is well known to lead to a limit cycle for certain ranges of values of the parameters involved in the problem. Within the tenets of the approximations made, reasonable agreement with the numerical plots can be achieved.

Item Type:Article
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ID Code:133818
Deposited On:30 Dec 2022 09:28
Last Modified:30 Dec 2022 09:28

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