Navigating climate complexity and its control via hyperchaotic dynamics in a 4D Caputo fractional model

Abstract

Abstract This interdisciplinary study critically analyzes current research, establishing a profound connection between sea water, sea ice, sea temperature, and surface temperature through a 4D hyperchaotic Caputo fractional differential equation. Emphasizing the collective impact on climate, focusing on challenges from anthropogenic global warming, the study scrutinizes theoretical aspects, including existence and uniqueness. Two sliding mode controllers manage chaos in this 4D fractional system, assessed amid uncertainties and disruptions. The global stability of these controlled systems is also confirmed, considering both commensurate and non-commensurate 4D fractional order. To demonstrate the intricate chaotic motion within the system, we employ the Lyapunov exponent and Poincare sections. Numerical simulations are conducted by using the predictor-corrector method. The effects of surface temperature on chaotic dynamics are discussed. The crucial role of sea ice reflection in climate stability is highlighted in two scenarios. Correlation graphs, comparing model and observational data using the predictor-corrector method, enhance the proposed 4D hyperchaotic model’s credibility. Subsequently, numerical simulations validate theoretical assertions about the controllers’ influence. These controllers indicate which variable significantly contributes to controlling the chaos.

Keywords

• 4D hyperchaotic attractor
• Chaos
• Caputo fractional derivative
• Global warming
• Predictor-corrector method