Eur. Phys. J. B 6, 529-536 (1998)
https://doi.org/10.1007/s100510050580

An analytical estimate of the period for the delayed logistic application and the Lotka-Volterra system

¹ Institut de Recherche sur les Phénomènes Hors Équilibre (CNRS, UMR 138) , Universités d'Aix-Marseille I et II, Service 252, Campus Universitaire de St. Jérôme, 13397 Marseille, Cedex 20, France
² Laboratoire des Écoulements Géophysiques et Industriels, Institut de Mécanique de Grenoble – CNRS, BP 53X, 38041 Grenoble Cedex, France

Corresponding author: ^a clanet@lrc.univ-mrs.fr

Received: 27 April 1998
Revised: 25 June 1998
Accepted: 29 June 1998
Published online: 15 December 1998

Abstract

We first introduce a simple and new method for the quantitative analysis of some nonlinear oscillating systems. It is shown that if the dynamics of the system reduces to piecewise exponential growth and exponential damping phases, then the amplitude and period of the motion can be computed with accuracy in the nonlinear regime without invoking linear stability arguments or perturbative expansions. This method is then successfully applied to the delayed logistic application and to the Lotka-Volterra prey-predator model. For both of these systems, we provide an accurate analytical expression for the period of the oscillations in the nonlinear regime.