Abstract:Recently, establishing proper dynamical models to describe the relationship among different chemical substances has become a vital theme in chemistry. In this present article, we set up a new fractional-order delayed glycolytic oscillator model. Utilizing the contraction mapping theorem, we explore the existence and uniqueness of the solution to the involved fractional glycolytic oscillator model with delay. By virtue of some suitable analytical skills, we discuss the non-negativeness of the solution to the es… Show more
“…Several other work on oscillatory solutions and their controllability in (integer and fractional) ordered dynamical systems are discussed in [20,33,45] and references therein.…”
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.
“…Several other work on oscillatory solutions and their controllability in (integer and fractional) ordered dynamical systems are discussed in [20,33,45] and references therein.…”
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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