A recurrence analysis of chaotic and non-chaotic solutions within a generalized nine-dimensional Lorenz model

Abstract

Abstract Based on recent studies using high-dimensional Lorenz models (LMs), a revised view on the nature of weather has been proposed as follows: the entirety of weather is a superset that consists of both chaotic and non-chaotic processes. We suggest that better predictability may be obtained for non-chaotic processes if they can be identified in advance. In this study, to achieve the goal, we generate recurrence plots (RPs) for classifying various types of solutions obtained using simplified and full versions of the generalized Lorenz model (GLM) with various M modes, including M = 3 , 5 , 7 , and 9. We first perform recurrence analyses of the following solutions: (1) a periodic solution and quasi-periodic solutions containing multiple incommensurate frequencies; (2) a temporal transition from an unstable solution to a limit cycle solution, which is an isolated closed orbit; and (3) the coexistence of two types of solutions such as a steady-state and a chaotic solution or a steady-state and limit cycle solution. Various types of solutions that coexist depend only on the initial conditions (ICs). Additionally, to effectively detect the dependence of the coexistence on ICs, we further complete the following: (1) We derive a new system, referred to as version 2 (V2), by decomposing a total field into a basic state and a perturbation. The V2 system is capable of depicting the linear and nonlinear evolution of perturbations that deviate from the basic state represented by a non-trivial critical point solution. (2) We perform ensemble runs with various ICs distributed over a hypersphere centered at a non-trivial critical point. (3) We produce recurrence plots for the ensemble runs using various radii for the hypersphere. The feasibility of applying the above method for analyzing African Easterly Waves (AEWs) is discussed near the end.