Research Unit of Automation and Applied Computer (UR-AIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon.
Department of Industrial Engineering and Maintenance, Polytechnic University of Mongo, Mongo, Chad.
Chaos. 2023 Jan;33(1):013139. doi: 10.1063/5.0115772.
In this work, we consider the geomagnetic field inversion model proposed by Gissinger et al. [Europhys. Lett. 90(4), 49001 (2010)], where a quadratic term is added for symmetry control purposes. The resulting system is explored in both symmetric and asymmetric modes of operation. In the symmetric case, we report a bursting phenomenon and heterogeneous multistability of six and four different attractors. We show that the model owns an offset adjustment feature. In the asymmetric case, the model develops different phenomena, such as the coexistence of (four and three) asymmetric attractors, asymmetric (periodic and chaotic) bursting oscillation, and transient asymmetric bursting phenomenon. The effect of symmetry breaking is also manifested in the bubbles of bifurcation. It is shown that this system can leave from the multistable state to a monostable state by adjusting the coupling parameter of a linear controller. Moreover, microcontroller-based implementation of the system is considered to check the correctness of the numerical results.
在这项工作中，我们考虑了 Gissinger 等人提出的地磁场所致反转模型[Europhys. Lett. 90(4), 49001 (2010)]，其中为了实现对称控制添加了二次项。研究了该系统在对称和非对称操作模式下的特性。在对称情况下，我们报告了突发现象和六个和四个不同吸引子的非均匀多稳定性。我们表明，该模型具有偏移调整功能。在非对称情况下，该模型会出现不同的现象，如（四个和三个）非对称吸引子共存、非对称（周期和混沌）突发振荡以及瞬态非对称突发现象。对称破缺的影响也体现在分岔的气泡中。结果表明，通过调整线性控制器的耦合参数，该系统可以从不稳定状态进入稳定状态。此外，还考虑了基于微控制器的系统实现，以检查数值结果的正确性。
