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.