Analytic structure of the Lorenz system

Abstract

The solutions of the Lorenz system are investigated by examination of their complex-time singularities. It is found that the location and type of singularity that occurs for complex time is critical in determining the behavior of the real-time solution. By direct expansion of the solution at a singularity its structure is determined. In general, the solutions are multiple valued in the neighborhood of a singularity; a property that is intimately related to the nonintegrability of the system. A numerical investigation is made of the analytic structure of solutions exhibiting turbulent bursts and undergoing period-doubling bifurcations.