Computational algorithms to study the chaotic dynamics of the logistic equation

Joo J.M. · Complexity and Fractality in Human Change and Beyond (2025)

Resumen

Understanding the behavior of the Logistic Equation is critical for those taking their first steps in the study of Chaos theory, and the best way to get familiar with chaotic dynamics is by developing computer programs to simulate it; with this in mind, this work deals mainly with the computational algorithms to study the dynamics of the mentioned equation. Implementing the computer programs with the algorithms in this work allows visualizing the dependence on initial conditions of the logistic equation, a feature typical of chaotic systems; this is made evident by running the logistic equation starting from slightly different initial conditions and may be graphically shown under slow motion on the computer screen. A special case of dependence on initial conditions is the Butterfly effect, which may also be visualized with the algorithms in this chapter. The reported algorithms also allow experimentally assessing up to five values of Feigenbaum's delta by plotting the equation's bifurcations cascade. This work also deals with the parabolicshaped Maps of Return of the logistic equation.

Instituciones: Universidad Nacional Mayor de San Marcos