New Approaches to Generalized Logistic Equation with Bifurcation Graph Generation Tool
Michał Ćmil, Dominik Strzałka, Franciszek Grabowski, Paweł Kuraś · Advances in Science and Technology – Research Journal · 2024
This paper proposed two new generalizations of the logistic function, each drawing on non-extensive thermodynamics, the q-logistic Equation and the logistic Equation of arbitrary order, respectively.It demonstrated the impact of chaos theory by integrating it with logistics Equations and revealed how minor parameter variations will change system behavior from deterministic to non-deterministic behavior.Moreover, this work presented BifDraw -a Python program for drawing bifurcation diagrams using classical logistic function and its generalizations illustrating the diversity of the system's response to the changes in the conditions.The research gave a pivotal role to the place of the logistic Equation in chaos theory by looking at its complicated dynamics and offering new generalizations that may be new in terms of thermodynamic basic states and entropy.Also, the paper investigated dynamics nature of the Equations and bifurcation diagrams in it which present complexity and the surprising dynamic systems features.The development of the BifDraw tool exemplifies the practical application of theoretical concepts, facilitating further exploration and understanding of logistic Equations within chaos theory.This study not only deepens the comprehension of logistic Equations and chaos theory, but also introduces practical tools for visualizing and analyzing their behaviors.