The butterfly effect in the chaotic nonlinear damped and forced oscillator

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

Resumen

This work reports the Butterfly Effect in the chaotic nonlinear damped and forced oscillator, which transitions to chaos employing cascades of period bifurcations. Altered chaotic events resulting from small changes in initial data taken as reference were obtained, and when compared to the original events, it was verified that the studied system experiences a Butterfly Effect. However, this does not manifest only as a final result; rather, the small changes in the initial data influence the evolution of the system, leading it down entirely different routes. It is observed that the cascades of period bifurcations in the altered events develop a notably different structure to that of the reference prototype events. It has also been observed that the evolution of the Lyapunov exponents during the flow of the altered systems follows remarkably different dynamics than that of the reference event. The more outstanding and enjoyable outcome of this investigation is that the number of periods the system oscillates with is raised when the initial input data is slightly increased. Additionally, some numerical data were collected during the computer simulation of the studied chaotic events, and these reflect significant differences when compared with the data from the prototypes.

Instituciones: Universidad Nacional Mayor de San Marcos