The role of elasticity on chaotic dynamics: insights from mechanics, immunology, ecology, and rheology

A. Jiménez-Casas, M. Castro, M. Villanueva Pesqueira

Mathematics Vol. 11, nº. 14, pp. 3099-1 - 3099-36

Summary:

Elasticity is commonly associated with regular oscillations, which are prevalent in various systems at different scales. However, chaotic oscillations are rarely connected to elasticity. While overdamped chaotic systems have received significant attention, there has been limited exploration of elasticity-driven systems. In this study, we investigate the influence of elasticity on the dynamics of chaotic systems by examining diverse models derived from mechanics, immunology, ecology, and rheology. Through numerical MATLAB simulations obtained by using an ode15s solver, we observe that elasticity profoundly alters the chaotic dynamics of these systems. As a result, we term the underlying equations as the elastic-Lorenz equations. Specifically, we extensively analyze a viscoelastic fluid confined within a closed-loop thermosyphon, considering general heat flux, to demonstrate the impact of the viscoelastic parameter on the model’s chaotic behavior. Our findings build upon prior research on the asymptotic behavior of this model by incorporating the presence of a viscoelastic fluid. The results highlight the non-trivial and non-monotonic role of elasticity in understanding the control, or lack thereof, of chaotic behavior across different scales.

Spanish layman's summary:

Esta investigación explora cómo la elasticidad es un fenómeno universal que no solo produce periodicidad sino que puede influir significativamente en el comportamiento caótico de sistemas mecánicos, biológicos o ecológicos.

English layman's summary:

This research explores how elasticity is a universal phenomenon that not only produces periodicity but can significantly influence the chaotic behavior of mechanical, biological or ecological systems.

Keywords: chaotic behavior; nonlinear dynamics; viscoelastic fluids; Lorenz-equations

JCR Impact Factor and WoS quartile: 2,300 - Q1 (2023)

DOI reference: https://doi.org/10.3390/math11143099

Published on paper: July 2023.

Published on-line: July 2023.

Citation:
A. Jiménez-Casas, M. Castro, M. Villanueva Pesqueira, The role of elasticity on chaotic dynamics: insights from mechanics, immunology, ecology, and rheology. Mathematics. Vol. 11, nº. 14, pp. 3099-1 - 3099-36, July 2023. [Online: July 2023]