Nonlinear Dynamics and Control of Driven Climate Variability and Ocean Heat Feedbacks

Title

Nonlinear Dynamics and Control of Driven Climate Variability and Ocean Heat Feedbacks

Creator

Sherly, K.; Veeresha, P.; Bade, Mahesh

Description

Abstract: Earths climate system is a highly complex and interconnected network governed by nonlinear interactions among the atmosphere, oceans, land, ice, and biosphere, where energy exchanges and feedback mechanisms play a dominant role. In recent decades, anthropogenic greenhouse gas emissions, especially carbon dioxide (), have significantly disrupted this balance, resulting in accelerated ocean heat uptake and persistent temperature anomalies. Determining the long-term dynamics of these interactions remains a critical challenge for accurate climate prediction and mitigation planning. This paper examines the combined dynamics of temperature anomaly, atmospheric concentration, and ocean heat content (OHC) using a novel mathematical approach. By employing the Caputo derivative to describe the model as a fractional-order dynamical system, hereditary effects and long-term dependencies that are inherent in climatic processes can be incorporated. Boundedness, existence and uniqueness of solutions, and both local and global stability are among the fundamental qualitative characteristics of the system that are investigated. To further illustrate stability behavior, streamline graphs are plotted. To ensure an accurate approximation of the fractional dynamics, numerical simulations are conducted using the Adams Bashforth Moulton (ABM) predictorcorrector method. Bifurcation analysis and computations of the Lyapunov exponent are performed to investigate the nonlinear properties of the system, exposing parameter regimes that behave chaotically for different fractional orders. Phase portraits in 2D and 3D show the intricate history of the climate variables. Additionally, to control chaotic oscillations, a sliding mode control approach is used. The findings highlight the promise of control theoretic techniques in climate dynamics by showing that the system is stabilized and chattering is successfully eliminated with the right control parameters. The results demonstrate that the fractional-order formulation provides enhanced capability in capturing long-term dependencies and nonlinear feedback mechanisms inherent in climate dynamics. The overall results show the models robustness as a theoretical framework for climate analysis and offer quantitative insights into the coupled climate systems long-term behavior. The models incorporation of nonlinear interactions among important variables improves the models interpretability and gives a more accurate picture of climate dynamics, which strengthens the foundation for assessing the effects of emissions and guiding the formulation of climate policy. King Abdulaziz University and Springer Nature Switzerland AG 2026.

Source

Earth Systems and Environment;

Date

01-01-2026

Publisher

Springer Science and Business Media Deutschland GmbH

Subject

Adams Bashforth Moulton Method (ABM); GHG Concentration of; Ocean Heat Content (OHC); Sliding Mode Controller (SMC); Streamline Plots; Temperature Anomaly

Coverage

Sherly K., Department of Mathematics, CHRIST University, Bengaluru, 560029, India; Veeresha P., Center for Mathematical Needs, Department of Mathematics, CHRIST University, Bengaluru, 560029, India; Bade M., Department of Environmental Science, Baylor University, Waco, 76706, TX, United States

Rights

Restricted Access; Hardcopy may be available in the library

Relation

ISSN: 25099426;

Format

online

Language

English

Type

Article

Identifier

https://doi.org/10.1007/s41748-026-01186-4

https://www.scopus.com/pages/publications/105040256957?origin=resultslist