Coexistence of chaotic and non-chaotic orbits in a new nine-dimensional lorenz model

Reyes T, Shen BW, Faghih-Naini S (2019)

Publication Type: Conference contribution

Publication year: 2019

Publisher: Springer

Pages Range: 239-255

Conference Proceedings Title: Springer Proceedings in Complexity

Event location: Rome IT

ISBN: 9783030152963

DOI: 10.1007/978-3-030-15297-0_22

Abstract

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 9DLM include: (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.

Authors with CRIS profile

Sara Faghih-Naini Lehrstuhl für Informatik 10 (Systemsimulation)

Involved external institutions

San Diego State University US United States (USA) (US)

How to cite

APA:

Reyes, T., Shen, B.-W., & Faghih-Naini, S. (2019). Coexistence of chaotic and non-chaotic orbits in a new nine-dimensional lorenz model. In Christos H. Skiadas, Ihor Lubashevsky (Eds.), Springer Proceedings in Complexity (pp. 239-255). Rome, IT: Springer.

MLA:

Reyes, Tiffany, Bo-Wen Shen, and Sara Faghih-Naini. "Coexistence of chaotic and non-chaotic orbits in a new nine-dimensional lorenz model." Proceedings of the 11th International Conference on Chaotic Modeling, Simulation and Applications, CHAOS 2018, Rome Ed. Christos H. Skiadas, Ihor Lubashevsky, Springer, 2019. 239-255.

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