A Transition to Chaos in Rucklidge Model of Double Convection

This paper considers a dissipative system of nonlinear ordinary differential equations proposed by A. M. Rucklidge to describe a process of double convection. Unlike the work of G. Chen, in which he made an attempt to classify, grounding on known L. P. Sil´nikov´s theorems, the whole variety of chaotic systems including the Rucklidge system, we demonstrate a new view on the process of transition to chaos in all dissipative systems of ODE, which is based on a subharmonic, homoclinic and heteroclinic cascades of bifurcations. The Rucklidge system undergoes a full analysis of singular points on a whole set of parameters´ values variation. Specifically, types of singular points, boarders of stability regions, as well as presented local bifurcations, are determined. By using numerical methods a consideration of scenarios of transition to chaos in the studied system with one bifurcation parameter variation is held.