Design of a fractional-order atmospheric model via a class of ACT-like chaotic system and its sliding mode chaos control

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.

An Application of the Caputo Fractional Domain in the Analysis of a COVID-19 Mathematical Model

“…Connecting the impact of vaccination with the BR number and analyzing the sensitivity of the BR number concerning the parameters is the specific contribution of this work. The numerical results obtained using the fractional Adams-Bashforth-Moultan (ABM) method are compatible with the Caputo FD [47][48][49][50][51].…”

A universal method for constructing n-dimensional polynomial hyperchaotic systems with any desired positive Lyapunov exponents

“…At present, the main methods for judging chaotic characteristics include phase trajectory (phase diagram) analysis, bifurcation diagram, Lyapunov exponent, fractional dimension analysis, complexity measurement, self-power spectrum analysis, and Stability analysis. etc [27][28][29]. In order to show the superiority of this map, a comparison with the new chaotic map in recent years is made in the discussion subsection.…”

A mathematical and sensitivity analysis of an HIV/AIDS infection model

“…Its origins can be traced back to the works of Newton and Leibniz and has grown into a powerful tool used to comprehend and model complex systems. Since its inception, fractional calculus has discovered a wide range of practical uses across various disciplines, such as physics, engineering, finance, and biology, see, [19][20][21][22][23][24]. The notion of fractional derivatives allows for a more comprehension understanding of systems and phenomena that exhibit fractal, anomalous, or memory-like behavior.…”