期刊
NONLINEAR DYNAMICS
卷 102, 期 4, 页码 2417-2431出版社
SPRINGER
DOI: 10.1007/s11071-020-06073-9
关键词
Invariant manifold; Separatrix; Stability; Tangency condition; Caputo fractional derivative
资金
- Science and Engineering Research Board (SERB), New Delhi, India [MTR/2017/000068]
- Department of Science and Technology (DST), New Delhi, India [IF170439]
Invariant manifolds are important sets arising in the stability theory of dynamical systems. In this article, we take a brief review of invariant sets. We provide some results regarding the existence of invariant lines and parabolas in planar polynomial systems. We provide the conditions for the invariance of linear subspaces in fractional-order systems. Further, we provide an important result showing the nonexistence of invariant manifolds (other than linear subspaces) in fractional-order systems.
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