The diffusionless Lorenz equations; Shil'nikov bifurcations and reduction to an explicit map (Q1581756)

The authors investigate an energetically closed model for convection, a version of the classical Lorenz model, in the limit for high Prandtl and Rayleigh numbers, i.e. diffusionless convection. They find an exact solution to this model, serving as a strong forcing limit, being a new integrable case of Lorenz equations. The bifurcations are studied mainly via a further reduction to an explicit analytic map and numerical exploration, which show that these essentially involve Shil'nivkov-type homoclinic bifurcations with a self similar behaviour in the parameter.