Chaos in a non-autonomous nonlinear system describing asymmetric water wheels
We derive a water wheel model from first principles under the assumption of an asymmetric water wheel for which the water in flow rate is in general unsteady (modeled by an arbitrary function of time). Our model allows one to recover the asymmetric water wheel with steady flow rate, as well as the s...
| Main Authors: | , |
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| Format: | Journal article |
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Springer
2018
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| _version_ | 1826303549259120640 |
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| author | Bhatt, A Van Gorder, R |
| author_facet | Bhatt, A Van Gorder, R |
| author_sort | Bhatt, A |
| collection | OXFORD |
| description | We derive a water wheel model from first principles under the assumption of an asymmetric water wheel for which the water in flow rate is in general unsteady (modeled by an arbitrary function of time). Our model allows one to recover the asymmetric water wheel with steady flow rate, as well as the symmetric water wheel, as special cases. Under physically reasonable assumptions we then reduce the underlying model into a non-autonomous nonlinear system. In order to determine parameter regimes giving chaotic dynamics in this non-autonomous nonlinear system, we consider an application of competitive modes analysis. In order to apply this method to a non-autonomous system, we are required to generalize the competitive modes analysis so that it is applicable to non-autonomous systems. The non-autonomous nonlinear water wheel model is shown to satisfy competitive modes conditions for chaos in certain parameter regimes, and we employ the obtained parameter regimes to construct the chaotic attractors. As anticipated, the asymmetric unsteady water wheel exhibits more disorder than does the asymmetric steady water wheel, which in turn is less regular than the symmetric steady state water wheel. Our results suggest that chaos should be fairly ubiquitous in the asymmetric water wheel model with unsteady inflow of water. |
| first_indexed | 2024-03-07T06:04:23Z |
| format | Journal article |
| id | oxford-uuid:ed53df8d-3282-400e-a08f-623f51c907b6 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:04:23Z |
| publishDate | 2018 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:ed53df8d-3282-400e-a08f-623f51c907b62022-03-27T11:24:09ZChaos in a non-autonomous nonlinear system describing asymmetric water wheelsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ed53df8d-3282-400e-a08f-623f51c907b6Symplectic Elements at OxfordSpringer2018Bhatt, AVan Gorder, RWe derive a water wheel model from first principles under the assumption of an asymmetric water wheel for which the water in flow rate is in general unsteady (modeled by an arbitrary function of time). Our model allows one to recover the asymmetric water wheel with steady flow rate, as well as the symmetric water wheel, as special cases. Under physically reasonable assumptions we then reduce the underlying model into a non-autonomous nonlinear system. In order to determine parameter regimes giving chaotic dynamics in this non-autonomous nonlinear system, we consider an application of competitive modes analysis. In order to apply this method to a non-autonomous system, we are required to generalize the competitive modes analysis so that it is applicable to non-autonomous systems. The non-autonomous nonlinear water wheel model is shown to satisfy competitive modes conditions for chaos in certain parameter regimes, and we employ the obtained parameter regimes to construct the chaotic attractors. As anticipated, the asymmetric unsteady water wheel exhibits more disorder than does the asymmetric steady water wheel, which in turn is less regular than the symmetric steady state water wheel. Our results suggest that chaos should be fairly ubiquitous in the asymmetric water wheel model with unsteady inflow of water. |
| spellingShingle | Bhatt, A Van Gorder, R Chaos in a non-autonomous nonlinear system describing asymmetric water wheels |
| title | Chaos in a non-autonomous nonlinear system describing asymmetric water wheels |
| title_full | Chaos in a non-autonomous nonlinear system describing asymmetric water wheels |
| title_fullStr | Chaos in a non-autonomous nonlinear system describing asymmetric water wheels |
| title_full_unstemmed | Chaos in a non-autonomous nonlinear system describing asymmetric water wheels |
| title_short | Chaos in a non-autonomous nonlinear system describing asymmetric water wheels |
| title_sort | chaos in a non autonomous nonlinear system describing asymmetric water wheels |
| work_keys_str_mv | AT bhatta chaosinanonautonomousnonlinearsystemdescribingasymmetricwaterwheels AT vangorderr chaosinanonautonomousnonlinearsystemdescribingasymmetricwaterwheels |