Generalized Full Order Observer Subject to Incremental Quadratic Constraint (IQC) for a Class of Fractional Order Chaotic Systems

Marwan, Muhammad; Abidin, Muhammad Zainul; Kalsoom, Humaira; Han, Maoan

doi:10.3390/fractalfract6040189

Cited by 6 publications

(7 citation statements)

References 51 publications

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“…The degree of chaos and unpredictability in a system is determined by its sensitivity to the initial conditions, the bifurcation parameter, and the dense oscillatory solutions. The aforementioned features of chaos in continuous systems are increasing its appeal by using it as a transmitter in secure communication 1 , path planing problems 2 – 4 , cryptography 5 and motion control 6 but apart from these applications in engineering, the term ”chaos” continues to be associated with negative impact in biological models and still remain as a villain such as Cancer 7 , Ebola 8 , 9 , Influenza 10 , 11 , HIV 12 , 13 and Parkinson 14 epidemic diseases models.…”

Section: Introductionmentioning

confidence: 99%

Generation of multi-scrolls in corona virus disease 2019 (COVID-19) chaotic system and its impact on the zero-covid policy

Marwan,

Han,

Khan

2023

Sci Rep

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In this paper, we discussed the impossibility of achieving zero-covid cases per day for all time with the help of fuzzy theory, while how a single case can trigger chaotic situation in the nearby city is elaborated using multi-scrolls. To accomplish this goal, we consider the number of new cases per day; $$x_{1}$$ x 1 to be the preferred state variable by restricting its value to the interval (0, 1). One can need to think of $$x_{1}$$ x 1 as a member of a fuzzy set and provide that set with appropriate membership functions. Moreover, how a single incident in one city can spread chaos to other cities is also addressed at length, using multi-scroll attractors and the signal excitation function. In addition, a bifurcation diagram of daily new instances vs the parameter $$\alpha _{1}$$ α 1 is shown, elaborating that daily new cases may show a decrease under strict rules and regulations, but can again lead to chaos. Apart from biologist, this paper can play vital role for engineers as well in a sense that, a signal function can be embedded in non-symmetric systems for the creation of multi-scroll attractors in all directions using a generalized algorithm that has been designed in the current work. Finally, it is our future target to show that the covid is leading towards influenza and will be no more dangerous as was in the past.

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Section: Introductionmentioning

confidence: 99%

Generation of multi-scrolls in corona virus disease 2019 (COVID-19) chaotic system and its impact on the zero-covid policy

Marwan,

Han,

Khan

2023

Sci Rep

Self Cite

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“…The significance of chaotic systems extends beyond mathematics and has a variety of implications in other disciplines. Marwan et al [27] applied the technique of observers with incremental quadratic constraints for fractional-ordered chaotic systems in 2022 as a method for the secure transmission of an image file. Guo et al [9] designed an algorithm with variable parameters for chaotic systems in 2021 and implemented it in RFID-based security.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Behavior of Lorenz-Based Chemical System under the Influence of Fractals

Marwan,

Xiong,

Han

et al. 2023

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This research examines a chaotic chemical reaction system based on the variation of the Lorenz system. This study demonstrates that although the first phase portraits of the chemical models under consideration and the Lorenz models are comparable, they do not fully follow all the features of the Lorenz system. Questions about the existence of fractals in systems based on chemical reactions are addressed in the current work. Moreover, we have worked on the hidden information inside in each wings of a chaotic system generated through fractal process, for the first time, with the aid of basin for fractals. Additionally, we looked closely at the dynamics of the model across the basin, which revealed additional details regarding the existence of hidden and cyclic attractors inside each wing. We also produced multi-wings for system (1) in the current study, demonstrating in a general manner that the number of cyclic attractors increase in a direct relation to the number of wings. Moreover, Julia approach is used to accomplish the work of multi-wings, whereas for searching cyclic attractors inside each extra wing, we have used fifteen million initial conditions and compiled them as a basin set. The data generated in this work is also provided within this paper for the ease of readers.

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“…In the beginning it was also linked with the butterfly effect. Several researchers used chaos as a positive term in their fields and have showed variety of its applications such as in engineering [ 16 , 17 ], secure communication [ 18 , 19 ], biology [ 20 , 21 ] and reference therein. But, in comparison with the importance of human lives, the term chaos is more dangerous.…”

Section: Introductionmentioning

confidence: 99%

Generalized external synchronization of networks based on clustered pandemic systems—The approach of Covid-19 towards influenza

Marwan,

Han,

Khan

2023

PLoS ONE

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Real-world models, like those used in social studies, epidemiology, energy transport, engineering, and finance, are often called “multi-layer networks.” In this work, we have described a controller that connects the paths of synchronized models that are grouped together in clusters. We did this using Lyapunov theory and a variety of coupled matrices to look into the link between the groups of chaotic systems based on influenza and covid-19. Our work also includes the use of external synchrony in biological systems. For example, we have explained in detail how the pandemic disease covid-19 will get weaker over time and become more like influenza. The analytical way to get these answers is to prove a theorem, and the numerical way is to use MATLAB to run numerical simulations.

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Generalized Full Order Observer Subject to Incremental Quadratic Constraint (IQC) for a Class of Fractional Order Chaotic Systems

Cited by 6 publications

References 51 publications

Generation of multi-scrolls in corona virus disease 2019 (COVID-19) chaotic system and its impact on the zero-covid policy

Generation of multi-scrolls in corona virus disease 2019 (COVID-19) chaotic system and its impact on the zero-covid policy

Chaotic Behavior of Lorenz-Based Chemical System under the Influence of Fractals

Generalized external synchronization of networks based on clustered pandemic systems—The approach of Covid-19 towards influenza

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