Fractal Fract, Vol. 7, Pages 791: Difference Equations and Julia Sets of Several Functions for Degenerate q-Sigmoid Polynomials

Fractal Fract, Vol. 7, Pages 791: Difference Equations and Julia Sets of Several Functions for Degenerate q-Sigmoid Polynomials

Fractal and Fractional doi: 10.3390/fractalfract7110791

Authors: Jung-Yoog Kang Cheon-Seoung Ryoo

In this article, we construct a new type of degenerate q-sigmoid (DQS) polynomial for sigmoid functions containing quantum numbers and find several difference equations related to it. We check how each point moves by iteratively synthesizing a quartic degenerate q-sigmoid (DQS) polynomial that appears differently depending on q in the space of a complex structure. We also construct Julia sets associated with quartic DQS polynomials and find their features. Based on this, we make some conjectures.