Chaotic oscillators with two types of semi-fractal equilibrium points: bifurcations, multistability, and fractal basins of attraction. (English) Zbl 1516.37038
Summary: 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 \(\mathbb{R}\) 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.
MSC:
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37G10 | Bifurcations of singular points in dynamical systems |
| 37G35 | Dynamical aspects of attractors and their bifurcations |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
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