Multi-scroll chaotic attractors and Poincaré maps via oscillating Gaussian potential

Mengran Li, Yunjie Tang, Qian Chen, Chengyue Zhang, Rong Gui () and Guanghui Cheng
Additional contact information
Mengran Li: Huazhong Agricultural University, College of Engineering
Yunjie Tang: Huazhong Agricultural University, College of Engineering
Qian Chen: Huazhong Agricultural University, College of Engineering
Chengyue Zhang: Huazhong Agricultural University, College of Engineering
Rong Gui: Huazhong Agricultural University, College of Engineering
Guanghui Cheng: Wuhan Polytechnic University, School of Electrical and Electronic Engineering

The European Physical Journal B: Condensed Matter and Complex Systems, 2025, vol. 98, issue 11, 1-15

Abstract: Abstract 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. Graphical abstract

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1140/epjb/s10051-025-01090-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:98:y:2025:i:11:d:10.1140_epjb_s10051-025-01090-2

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/s10051-025-01090-2

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().