Complex dynamical analysis of fractional differences Willamowski–Röossler chemical reaction model in time-scale analysis
Real mechanisms that are advancing in a complex network exhibit chaotic behaviour. This behaviour is crucial in physical and complex systems involving numerical modelling frameworks because it essentially determines the framework’s evolutionary process. In this context, notwithstanding its difficult...
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| Format: | Article |
| Language: | English |
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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/S2211379723008161 |
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| author | Yu-Ming Chu Taher Alzahrani Saima Rashid Hisham Alhulayyil Waleed Rashidah Shafiq ur Rehman |
| author_facet | Yu-Ming Chu Taher Alzahrani Saima Rashid Hisham Alhulayyil Waleed Rashidah Shafiq ur Rehman |
| author_sort | Yu-Ming Chu |
| collection | DOAJ |
| description | Real mechanisms that are advancing in a complex network exhibit chaotic behaviour. This behaviour is crucial in physical and complex systems involving numerical modelling frameworks because it essentially determines the framework’s evolutionary process. In this context, notwithstanding its difficulty, the potential of intentional oversight of the phenomenon has feasible effects; this is why theoretical approaches are advantageous in such scenarios. This study investigates the functioning of a Willamowski–Rössler (W–R) mechanism, including the synchronization of two minimal W–R structures depending on the responsive suggestion technique for regulation, with the purpose of achieving chaos influence in chemical interactions. We investigate the reliability of the steady state at various fractional order (FO) factors. Employing maximum Lyapunov exponents (MLEs), phase depictions, bifurcation schematics, the 0–1 evaluation and approximated entropy, it is demonstrated that adjusting the FOs causes a system’s behavioural pattern to undergo a transition from steady to chaotic. In addition to demonstrating that the proposed scheme fits chaotically under certain circumstances, simulation outcomes demonstrate that mathematical modelling is used to illustrate theoretical debates. To verify that the community detects chaos, the MLE and bifurcation illustrations, whose hallmark factors are plotted, display erratic behaviour while effectively attempting to control the chaos. |
| first_indexed | 2024-03-11T07:34:04Z |
| format | Article |
| id | doaj.art-89e58060d8354c0884e05661a4435ec5 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-11T07:34:04Z |
| publishDate | 2023-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-89e58060d8354c0884e05661a4435ec52023-11-17T05:26:15ZengElsevierResults in Physics2211-37972023-11-0154107023Complex dynamical analysis of fractional differences Willamowski–Röossler chemical reaction model in time-scale analysisYu-Ming Chu0Taher Alzahrani1Saima Rashid2Hisham Alhulayyil3Waleed Rashidah4Shafiq ur Rehman5School of Science, Hunan City University, Yiyang 413000, P.R. ChinaInformation Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaDepartment of Mathematics, Government College University, Faisalabad 38000, Pakistan; Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Corresponding author at: Department of Mathematics, Government College University, Faisalabad 38000, Pakistan.Information Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaInformation Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaInformation Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaReal mechanisms that are advancing in a complex network exhibit chaotic behaviour. This behaviour is crucial in physical and complex systems involving numerical modelling frameworks because it essentially determines the framework’s evolutionary process. In this context, notwithstanding its difficulty, the potential of intentional oversight of the phenomenon has feasible effects; this is why theoretical approaches are advantageous in such scenarios. This study investigates the functioning of a Willamowski–Rössler (W–R) mechanism, including the synchronization of two minimal W–R structures depending on the responsive suggestion technique for regulation, with the purpose of achieving chaos influence in chemical interactions. We investigate the reliability of the steady state at various fractional order (FO) factors. Employing maximum Lyapunov exponents (MLEs), phase depictions, bifurcation schematics, the 0–1 evaluation and approximated entropy, it is demonstrated that adjusting the FOs causes a system’s behavioural pattern to undergo a transition from steady to chaotic. In addition to demonstrating that the proposed scheme fits chaotically under certain circumstances, simulation outcomes demonstrate that mathematical modelling is used to illustrate theoretical debates. To verify that the community detects chaos, the MLE and bifurcation illustrations, whose hallmark factors are plotted, display erratic behaviour while effectively attempting to control the chaos.http://www.sciencedirect.com/science/article/pii/S2211379723008161Willamowski–Rössler systemFractional difference equationChaotic attractorsBifurcationLyapunov exponentComplex systems |
| spellingShingle | Yu-Ming Chu Taher Alzahrani Saima Rashid Hisham Alhulayyil Waleed Rashidah Shafiq ur Rehman Complex dynamical analysis of fractional differences Willamowski–Röossler chemical reaction model in time-scale analysis Results in Physics Willamowski–Rössler system Fractional difference equation Chaotic attractors Bifurcation Lyapunov exponent Complex systems |
| title | Complex dynamical analysis of fractional differences Willamowski–Röossler chemical reaction model in time-scale analysis |
| title_full | Complex dynamical analysis of fractional differences Willamowski–Röossler chemical reaction model in time-scale analysis |
| title_fullStr | Complex dynamical analysis of fractional differences Willamowski–Röossler chemical reaction model in time-scale analysis |
| title_full_unstemmed | Complex dynamical analysis of fractional differences Willamowski–Röossler chemical reaction model in time-scale analysis |
| title_short | Complex dynamical analysis of fractional differences Willamowski–Röossler chemical reaction model in time-scale analysis |
| title_sort | complex dynamical analysis of fractional differences willamowski roossler chemical reaction model in time scale analysis |
| topic | Willamowski–Rössler system Fractional difference equation Chaotic attractors Bifurcation Lyapunov exponent Complex systems |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723008161 |
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