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Nonexistence of invariant manifolds in fractional-order dynamical systems |
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| Authors: | Bhalekar Sachin Patil Madhuri |
| Institution: | 1.School of Mathematics and Statistics, University of Hyderabad, Hyderabad, 500046, India ;2.Department of Mathematics, Shivaji University, Kolhapur, 416004, India ; |
| Abstract: | 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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