Linear Augmentation for Stabilizing Stationary Solutions: Potential Pitfalls and Their Application.
Linear augmentation has recently been shown to be effective in targeting desired stationary solutions, suppressing bistablity, in regulating the dynamics of drive response systems and in controlling the dynamics of hidden attractors. The simplicity of the procedure is the main highlight of this sche...
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2015-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC4636295?pdf=render |
| _version_ | 1819266443599937536 |
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| author | Rajat Karnatak |
| author_facet | Rajat Karnatak |
| author_sort | Rajat Karnatak |
| collection | DOAJ |
| description | Linear augmentation has recently been shown to be effective in targeting desired stationary solutions, suppressing bistablity, in regulating the dynamics of drive response systems and in controlling the dynamics of hidden attractors. The simplicity of the procedure is the main highlight of this scheme but questions related to its general applicability still need to be addressed. Focusing on the issue of targeting stationary solutions, this work demonstrates instances where the scheme fails to stabilize the required solutions and leads to other complicated dynamical scenarios. Examples from conservative as well as dissipative systems are presented in this regard and important applications in dissipative predator-prey systems are discussed, which include preventative measures to avoid potentially catastrophic dynamical transitions in these systems. |
| first_indexed | 2024-12-23T21:01:21Z |
| format | Article |
| id | doaj.art-e4965d9ff4964cefb52e55f05e9c717e |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-23T21:01:21Z |
| publishDate | 2015-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-e4965d9ff4964cefb52e55f05e9c717e2022-12-21T17:31:22ZengPublic Library of Science (PLoS)PLoS ONE1932-62032015-01-011011e014223810.1371/journal.pone.0142238Linear Augmentation for Stabilizing Stationary Solutions: Potential Pitfalls and Their Application.Rajat KarnatakLinear augmentation has recently been shown to be effective in targeting desired stationary solutions, suppressing bistablity, in regulating the dynamics of drive response systems and in controlling the dynamics of hidden attractors. The simplicity of the procedure is the main highlight of this scheme but questions related to its general applicability still need to be addressed. Focusing on the issue of targeting stationary solutions, this work demonstrates instances where the scheme fails to stabilize the required solutions and leads to other complicated dynamical scenarios. Examples from conservative as well as dissipative systems are presented in this regard and important applications in dissipative predator-prey systems are discussed, which include preventative measures to avoid potentially catastrophic dynamical transitions in these systems.http://europepmc.org/articles/PMC4636295?pdf=render |
| spellingShingle | Rajat Karnatak Linear Augmentation for Stabilizing Stationary Solutions: Potential Pitfalls and Their Application. PLoS ONE |
| title | Linear Augmentation for Stabilizing Stationary Solutions: Potential Pitfalls and Their Application. |
| title_full | Linear Augmentation for Stabilizing Stationary Solutions: Potential Pitfalls and Their Application. |
| title_fullStr | Linear Augmentation for Stabilizing Stationary Solutions: Potential Pitfalls and Their Application. |
| title_full_unstemmed | Linear Augmentation for Stabilizing Stationary Solutions: Potential Pitfalls and Their Application. |
| title_short | Linear Augmentation for Stabilizing Stationary Solutions: Potential Pitfalls and Their Application. |
| title_sort | linear augmentation for stabilizing stationary solutions potential pitfalls and their application |
| url | http://europepmc.org/articles/PMC4636295?pdf=render |
| work_keys_str_mv | AT rajatkarnatak linearaugmentationforstabilizingstationarysolutionspotentialpitfallsandtheirapplication |