Nonexistence of invariant manifolds in fractional-order dynamical systems

Nonexistence of invariant manifolds in fractional-order dynamical systems

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 inv...

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Veröffentlicht in:Nonlinear dynamics 2020-12, Vol.102 (4), p.2417-2431
Hauptverfasser: Bhalekar, Sachin, Patil, Madhuri
Format: Artikel
Sprache:eng
Schlagworte:
Automotive Engineering
Classical Mechanics
Control
Dynamic stability
Dynamical Systems
Engineering
Invariants
Manifolds
Mechanical Engineering
Original Paper
Parabolas
Polynomials
Subspaces
Vibration
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Zusammenfassung: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.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-06073-9