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.
ABSTRACT
Investigation of the dynamical behavior related to environmental phenomena has received much attention across a variety of scientific domains. One such phenomenon is global warming. The main causes of global warming, which has detrimental effects on our ecosystem, are mainly excess greenhouse gases and temperature. Looking at the significance of this climatic event, in this study, we have connected the ACT-like model to three climatic components, namely, permafrost thaw, temperature, and greenhouse gases in the form of a Caputo fractional differential equation, and analyzed their dynamics. The theoretical aspects, such as the existence and uniqueness of the obtained solution, are examined. We have derived two different sliding mode controllers to control chaos in this fractional-order system. The influences of these controllers are analyzed in the presence of uncertainties and external disturbances. In this process, we have obtained a new controlled system of equations without and with uncertainties and external disturbances. Global stability of these new systems is also established. All the aspects are examined for commensurate and non-commensurate fractional-order derivatives. To establish that the system is chaotic, we have taken the assistance of the Lyapunov exponent and the bifurcation diagram with respect to the fractional derivative. To perform numerical simulation, we have identified certain values of the parameters where the system exhibits chaotic behavior. Then, the theoretical claims about the influence of the controller on the system are established with the help of numerical simulations.