The effect of climate change on the dynamics of a modified surface energy balance-mass balance model of Cryosphere under the frame of a non-local operator
One of the major causes of the intermittent nature of long-term climate changes is the interaction between the surface energy balance and the mass balance of the Cryosphere. In this paper, the pre-existing surface energy balance-mass balance model of the Cryosphere is modified by incorporating the r...
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Elsevier
2023-11-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723008240 |
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| author | Arkaprovo Chakraborty P. Veeresha Armando Ciancio Haci Mehmet Baskonus Mansoor Alsulami |
| author_facet | Arkaprovo Chakraborty P. Veeresha Armando Ciancio Haci Mehmet Baskonus Mansoor Alsulami |
| author_sort | Arkaprovo Chakraborty |
| collection | DOAJ |
| description | One of the major causes of the intermittent nature of long-term climate changes is the interaction between the surface energy balance and the mass balance of the Cryosphere. In this paper, the pre-existing surface energy balance-mass balance model of the Cryosphere is modified by incorporating the radiative forcing of CO2 to observe the effect of global warming on the nature of the previous model. The modified model is generalized using Caputo’s non-local operator. The stability of the new model is analyzed at all the equilibrium points and also it is shown that there exists a unique and bounded solution for the modified system. Using bifurcation analysis and calculating the values of Lyapunov exponents for different fractional orders of the modified system, it is found that the system exhibits chaos for certain values of the radiating forcing of CO2 To observe and visualize the changes in the nature of the new model, the system is solved using the highly efficient 7th-order Runge–Kutta method. It is observed that with the inclusion of the radiative forcing of CO2, the nature of the system changes from asymptotically stable to chaotic as we decrease the order of the system. The Poincare map shows that the modified model even has characteristics of a strange attractor which is highly chaotic. The system becomes unstable when the value of the radiative forcing of CO2 is increased. As a result, the predictive power of the surface energy balance-mass balance model of the Cryosphere decreases. In addition to providing insights into the transition from stability to chaos in the Cryosphere model due to CO2 radiative forcing, this research offers a deeper understanding of the intricate interplay between climate dynamics and complex systems behavior. |
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| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-11T07:33:46Z |
| publishDate | 2023-11-01 |
| publisher | Elsevier |
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| series | Results in Physics |
| spelling | doaj.art-49d51f7958b342d4a064253b62d0db062023-11-17T05:26:16ZengElsevierResults in Physics2211-37972023-11-0154107031The effect of climate change on the dynamics of a modified surface energy balance-mass balance model of Cryosphere under the frame of a non-local operatorArkaprovo Chakraborty0P. Veeresha1Armando Ciancio2Haci Mehmet Baskonus3Mansoor Alsulami4Department of Mathematics, CHRIST (Deemed to be University), Bengaluru 560029, IndiaDepartment of Mathematics, CHRIST (Deemed to be University), Bengaluru 560029, IndiaUniversità degli Studi di Messina, Dipartimento di Scienze Biomediche, Odontoiatriche e delle Immagini Morfologiche e Funzionali, Messina, ItalyDepartment of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa, Turkey; Corresponding author.Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaOne of the major causes of the intermittent nature of long-term climate changes is the interaction between the surface energy balance and the mass balance of the Cryosphere. In this paper, the pre-existing surface energy balance-mass balance model of the Cryosphere is modified by incorporating the radiative forcing of CO2 to observe the effect of global warming on the nature of the previous model. The modified model is generalized using Caputo’s non-local operator. The stability of the new model is analyzed at all the equilibrium points and also it is shown that there exists a unique and bounded solution for the modified system. Using bifurcation analysis and calculating the values of Lyapunov exponents for different fractional orders of the modified system, it is found that the system exhibits chaos for certain values of the radiating forcing of CO2 To observe and visualize the changes in the nature of the new model, the system is solved using the highly efficient 7th-order Runge–Kutta method. It is observed that with the inclusion of the radiative forcing of CO2, the nature of the system changes from asymptotically stable to chaotic as we decrease the order of the system. The Poincare map shows that the modified model even has characteristics of a strange attractor which is highly chaotic. The system becomes unstable when the value of the radiative forcing of CO2 is increased. As a result, the predictive power of the surface energy balance-mass balance model of the Cryosphere decreases. In addition to providing insights into the transition from stability to chaos in the Cryosphere model due to CO2 radiative forcing, this research offers a deeper understanding of the intricate interplay between climate dynamics and complex systems behavior.http://www.sciencedirect.com/science/article/pii/S2211379723008240CryosphereSurface energy balanceMass balanceCaputo fractional derivativeBifurcationLyapunov exponent |
| spellingShingle | Arkaprovo Chakraborty P. Veeresha Armando Ciancio Haci Mehmet Baskonus Mansoor Alsulami The effect of climate change on the dynamics of a modified surface energy balance-mass balance model of Cryosphere under the frame of a non-local operator Results in Physics Cryosphere Surface energy balance Mass balance Caputo fractional derivative Bifurcation Lyapunov exponent |
| title | The effect of climate change on the dynamics of a modified surface energy balance-mass balance model of Cryosphere under the frame of a non-local operator |
| title_full | The effect of climate change on the dynamics of a modified surface energy balance-mass balance model of Cryosphere under the frame of a non-local operator |
| title_fullStr | The effect of climate change on the dynamics of a modified surface energy balance-mass balance model of Cryosphere under the frame of a non-local operator |
| title_full_unstemmed | The effect of climate change on the dynamics of a modified surface energy balance-mass balance model of Cryosphere under the frame of a non-local operator |
| title_short | The effect of climate change on the dynamics of a modified surface energy balance-mass balance model of Cryosphere under the frame of a non-local operator |
| title_sort | effect of climate change on the dynamics of a modified surface energy balance mass balance model of cryosphere under the frame of a non local operator |
| topic | Cryosphere Surface energy balance Mass balance Caputo fractional derivative Bifurcation Lyapunov exponent |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723008240 |
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