https://doi.org/10.1140/epjp/s13360-023-04296-4
Regular Article
Bursting oscillations and bifurcation mechanisms in a 4D non-smooth Sprott C model
School of Mathematical Sciences, Jiangsu University, 301 Xuefu Road, 212013, Zhenjiang, Jiangsu, China
Received:
3
June
2023
Accepted:
18
July
2023
Published online:
27
July
2023
Non-smooth factors and multiscale couplings are commonly present in daily life and engineering applications. In this research paper, our focus lies in exploring the mechanism behind bursting oscillations and the intricate dynamical properties resulting from diverse scale couplings within the frequency domain of Filippov systems. Based on an improved Sprott C model, we provide equilibrium branches and bifurcations of subsystems in different regions for two typical parameter cases. The transformed phase portrait exhibits the presence of asymmetric bursting attractors. By superimposing the transformed phase portrait with the equilibrium branches and bifurcation diagram, we can uncover the underlying generation mechanism of two distinct bursting modes. Our findings indicate that both equilibrium branches and bifurcations have a significant impact not only on the structure of bursting oscillation attractors but also on the configuration of quiescent states or spiking states, as well as the transition mechanism between these states. As a result, various bursting modes can emerge due to these factors. In this system, as a result of the presence of the slow passage effect, when the trajectory traverses the stable equilibrium branch towards the bifurcation point, it does not immediately enter into oscillatory behavior. Instead, it continues along the unstable branch for a certain duration before eventually transitioning into oscillations. Moreover, we can observe sliding behavior along the non-smooth interface. It is worth noting that, unlike most Filippov systems, the sliding behavior of this system is not caused by the sliding region on the boundary, but rather because of the attraction by the stable equilibrium branch. Our research results enrich the study of the complex dynamical behavior of high-dimensional non-smooth systems under different scales of coupling and deepen the understanding of the sliding behavior of Filippov systems on the boundary.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. 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.
