Manal Menchih, Khalid Hilal, Ahmed Kajouni, Mohammad Esmael Samei
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Chaotic Dynamics of Conformable Maturity-Structured Cell Population Models
The primary aim of this study is to analyze the chaotic dynamics of a conformable maturity structured cell partial differential equation of order \(z\in (0,1)\), which extends the classical Lasota equation. To examine the chaotic behavior of our model’s solution, we initially extend certain criteria of linear chaos to conformable calculus. This extension is crucial because the solution of our model does not generate a classical semigroup but rather a \(c_0\)-z-semigroup. For the velocity term of our model, \(B(\mathfrak {w})=\mu \mathfrak {w}\), where \(\mu \in \mathbb {C}\), and the term source \(g(\mathfrak {w}, \vartheta (\textsf{r}, \mathfrak {w}))\), we utilize spectral properties of the z-infinitesimal generator to demonstrate chaotic behavior in the space \(C(\textrm{J}_0, \mathbb {C})\), \(\textrm{J}_0:=[0,+\infty )\). Furthermore, by employing conformable admissible weight functions and setting \(B(\mathfrak {w})=1\), we establish chaos in the solution z-semigroup, this time within the space \(C_{0}(\textrm{J}_0, \mathbb {C})\).
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.