Chaotic oscillators with two types of semi-fractal equilibrium points: Bifurcations, multistability, and fractal basins of attraction

Two new three-dimensional chaotic oscillators are introduced in this paper. Each oscillator has a different type of semi-fractal equilibrium curve: one with an R domain semi-fractal curve and one with a circular parametric semi-fractal curve. Both oscillators have the Weierstrass function as a basis in their equations. Different properties of these oscillators, such as bifurcation, multistability, and fractal basins of attraction, are investigated. The proposed system, like the chaotic systems of the references (such as systems with no equilibria and systems with a stable equilibrium) is typical. We believe such a chaotic system with fractal equilibria was not proposed before. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper introduces two new three-dimensional chaotic oscillators, each with a different type of semi-fractal equilibrium curve: one with an R domain semi-fractal curve and one with a circular parametric semi-fractal curve. Both oscillators utilize the Weierstrass function as a basis in their equations. Various properties of these oscillators, including bifurcation, multistability, and fractal basins of attraction, are investigated. The proposed system is considered typical, similar to chaotic systems in previous references, but with the addition of fractal equilibria.