Modifying some foliated dynamical systems to guide their trajectories to specified sub-manifolds

Vaidya, Prabhakar G and Majumdar, Swarnali (2011) Modifying some foliated dynamical systems to guide their trajectories to specified sub-manifolds. Mathematica Bohemica, 136 (4). pp. 439-448.

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Abstract: We show that dynamical systems in inverse problems are sometimes foliated if the embedding dimension is greater than the dimension of the manifold on which the system resides. Under this condition, we end up reaching different leaves of the foliation if we start from different initial conditions. For some of these cases we have found a method by which we can asymptotically guide the system to a specific leaf even if we start from an initial condition which corresponds to some other leaf. We demonstrate the method by two examples. In the chosen cases of the harmonic oscillator and Duffing’s oscillator we find an alternative set of equations which represent a collapsed foliation, such that no matter what initial conditions we choose, the system would asymptotically reach the same desired sub-manifold of the original system. This process can lead to cases for which a system begins in a chaotic region, but is guided to a periodic region and vice versa. It may also happen that we could move from an orbit of one period to an orbit of another period.
Item Type: Journal Paper
Keywords: manifold, foliation, duffing oscillator, Classification (MSC 2010): 34D35, 34A55
Subjects: School of Natural and Engineering Sciences > Complex Systems
Doctoral Programme > PhD Scholar Publications
Date Deposited: 31 Mar 2021 11:56
Last Modified: 05 Jun 2021 17:51
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    Funders: Department of Science and Technology (DST), Government of India
    Projects: UNSPECIFIED

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