Stable/unstable slow integral manifolds in critical cases

8th Workshop on Multi-Rate Processes and Hysteresis;HSFS Workshop (Hysteresis and Slow-Fast Systems)

Shchepakina, Elena^1

Department of Technical Cybernetics, Samara National Research University, Moskovskoe shosse, Russian Federation.34, Samara

443086, Russia^1

关键词: Critical case;    Hindmarsh rose;    Integral manifold;    Multiple changes;    Singularly perturbed systems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/811/1/012016/pdf
DOI  :  10.1088/1742-6596/811/1/012016

来源: IOP

【 摘 要 】

The paper deals with the problem of a construction of global stable/unstable slow integral manifolds of the singularly perturbed systems in critical cases. In addition to the well-known critical cases a novel scenario of the stability change of the slow integral manifold is considered. All three critical cases leading to the change of the stability are discussed via the Hindmarsh-Rose dynamic model. It is shown that the suitable choice of the additional parameters of the system yields the slow integral manifold with multiple change of its stability.