## Title data

Shen, Bo-Wen ; Reyes, Tiffany ; Faghih-Naini, Sara:

**Coexistence of Chaotic and Non-chaotic Orbits in a New Nine-Dimensional Lorenz Model.**

*In:* Skiadas, Christos H. ; Lubashevsky, Ihor
(ed.):
11th Chaotic Modeling and Simulation International Conference. -
Cham
: Springer
,
2019
. - pp. 239-255

ISBN 978-3-030-15296-3

DOI: https://doi.org/10.1007/978-3-030-15297-0_22

## Abstract in another language

In this study, we present a new nine-dimensional Lorenz model (9DLM) that requires a larger critical value for the Rayleigh parameter (a rc of 679.8) for the onset of chaos, as compared to a rc of 24.74 for the 3DLM, a rc of 42.9 for the 5DLM, and a rc 116.9 for the 7DLM. Major features within the 9DLMinclude: (1) the coexistence of chaotic and non-chaotic orbits with moderate Rayleigh parameters, and (2) the coexistence of limit cycle/torus orbits and spiral sinks with large Rayleigh parameters. Version 2 of the 9DLM, referred to as the 9DLM-V2, is derived to show that: (i) based on a linear stability analysis, two non-trivial critical points are stable for all Rayleigh parameters greater than one; (ii) under non-dissipative and linear conditions, the extended nonlinear feedback loop produces four incommensurate frequencies; and (iii) for a stable orbit, small deviations away from equilibrium (e.g., the stable critical point) do not have a significant impact on orbital stability. Based on our results, we suggest that the entirety of weather is a superset that consists of both chaotic and non-chaotic processes.