https://doi.org/10.1140/epjp/s13360-024-05295-9
Regular Article
Controllable multi-scroll with multi-wing, grid-scroll, and multi-directional grid-scroll chaotic attractors in a chaotic system with implicit Duffing equation
1
College of Engineering, Huazhong Agricultural University, 430070, Wuhan, China
2
School of Electrical and Electronic Engineering, Wuhan Polytechnic University, 430048, Wuhan, China
Received:
21
February
2024
Accepted:
20
May
2024
Published online:
6
June
2024
Multi-scroll chaotic systems have great theoretical significance and engineering application value. Here, we report a chaotic system which can generate controllable multi-scroll chaotic attractors with multiple wings by introducing sine function into the x, y, and z directions. The system can generate 2D grid-scroll chaotic attractors due to the same mechanism of chaos in the x and y directions. Although the system only possesses one equilibrium point in this case, the locations of the scrolls and wings can be determined based on the potential well distribution as the system implies the Duffing equation. However, the generation of multi-scroll chaotic attractors in the z direction is ascribed to the presence of two types of equilibrium points in the system, namely, unstable index-1 and index-2 saddle-foci. Due to different mechanisms for the generation of multi-scroll chaotic attractors, the system cannot generate 3D grid-scroll chaotic attractors, but can generate multi-directional grid-scroll chaotic attractors with a wider coverage by using a non-autonomous approach. The time series of 2D grid-scroll chaotic attractors exhibits intermittent chaos. Then, the amplitude of the sine function in the z direction can be manipulated to control the intermittent chaos, making it either more stable (stable point) or more chaotic (largest Lyapunov exponent exceeding 30). Damping coefficient is introduced to control the number of scrolls and wings based on the Duffing equation. Finally, the physical feasibility of the system was verified through circuit experiments based on microcontrollers.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.