Determining the Critical Point of a Sigmoidal Curve via its Fourier Transform

5th International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Bilge, Ayse Humeyra^1 ; Ozdemir, Yunus^1

Faculty of Engineering and Natural Sciences, Kadir Has University, Department of Mathematics, Anadolu University, Istanbul, Eskisehir, Turkey^1

关键词: A-monotone;    Gel point;    Junction point;    Limit points;    Rate of change;    Sigmoidal curves;    Sol-gel transitions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/738/1/012062/pdf
DOI  :  10.1088/1742-6596/738/1/012062

来源: IOP

【 摘 要 】

A sigmoidal curve y(t) is a monotone increasing curve such that all derivatives vanish at infinity. Let tnbe the point where the nth derivative of y(t) reaches its global extremum. In the previous work on sol-gel transition modelled by the Susceptible-Infected- Recovered (SIR) system, we observed that the sequence {tn} seemed to converge to a point that agrees qualitatively with the location of the gel point [2]. In the present work we outline a proof that for sigmoidal curves satisfying fairly general assumptions on their Fourier transform, the sequence {tn} is convergent and we call it "the critical point of the sigmoidal curve". In the context of phase transitions, the limit point is interpreted as a junction point of two different regimes where all derivatives undergo their highest rate of change.