https://doi.org/10.1140/epjb/s10051-025-01090-2
Research - Statistical and Nonlinear Physics
Multi-scroll chaotic attractors and Poincaré maps via oscillating Gaussian potential
1
College of Engineering, Huazhong Agricultural University, 430070, Wuhan, China
2
School of Electrical and Electronic Engineering, Wuhan Polytechnic University, 430048, Wuhan, China
Received:
28
April
2025
Accepted:
7
November
2025
Published online:
19
November
2025
Designing chaotic systems based on the physical mechanism to generate controllable chaotic attractors with specific structures is instrumental in advancing our understanding of chaotic dynamics and promoting engineering applications. By introducing the oscillating Gaussian potential, a novel Duffing system is developed, in which the stability of equilibrium points undergoes periodic alternation. This alternation effectively increases the total number of both stable and unstable points, thereby leading to the generation of additional scrolls in the chaotic attractor. Leveraging the physical interpretability of the Duffing framework, the number of scrolls can be controlled by tuning key parameters, including the potential difference, oscillation amplitude and frequency, and damping coefficient, as confirmed by bifurcation analysis. The Poincaré maps exhibit a multi-scroll structure that evolves synchronously with the potential well oscillation, demonstrating the unique dynamic behavior induced by alternating equilibrium points. In this regime, particles are successively attracted and repelled as the equilibrium points periodically switch between stable and unstable states. The system also exhibits both homogeneous and heterogeneous multistability. Finally, our results were verified through hardware experiments based on microcontrollers.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjb/s10051-025-01090-2.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
