Heteroclinic Orbit, Forced Lorenz System, and Chaos

Abstract

Forced Lorenz system, important in modeling of monsoonlike phenomena, is analyzed for the existence of heteroclinic orbit. This is done in the light of the suggested new mechanism for the onset of chaos by and (2006, “Finding Homoclinic and Heteroclinic Contours of Singular Points of Nonlinear Systems of Ordinary Differential Equations,” Diff. Eq., 39, pp. 1593–1602), where heteroclinic orbits plays important and dominant roles. The analysis is performed based on the theory laid down by Shilnikov. An analytic expression in the form of uniformly convergent series is obtained. The same orbit is also obtained numerically by a technique enunciated by Magnitskii and Sidorov, reproducing the necessary important features.