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.
| 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 |
| Official URL: |
https://mb.math.cas.cz/full/136/4/mb136_4_10.pdf |
| Related URLs: |
|
| Funders: |
Department of Science and Technology (DST), Government of India |
| Projects: |
UNSPECIFIED |
| DOI: |
|
| URI: |
http://eprints.nias.res.in/id/eprint/2078 |
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