Control of traveling-wave oscillations and bifurcation behavior in central pattern generators
Understanding synchronous and traveling-wave oscillations, particularly as they relate to transitions between different types of behavior, is a central problem in modeling biological systems. Here, we address this problem in the context of central pattern generators (CPGs). We use contraction theory...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2013
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| Online Access: | http://hdl.handle.net/1721.1/76203 https://orcid.org/0000-0002-7161-7812 |
| _version_ | 1826217435256061952 |
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| author | Landsman, Alexandra S. Slotine, Jean-Jacques E. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Landsman, Alexandra S. Slotine, Jean-Jacques E. |
| author_sort | Landsman, Alexandra S. |
| collection | MIT |
| description | Understanding synchronous and traveling-wave oscillations, particularly as they relate to transitions between different types of behavior, is a central problem in modeling biological systems. Here, we address this problem in the context of central pattern generators (CPGs). We use contraction theory to establish the global stability of a traveling-wave or synchronous oscillation, determined by the type of coupling. This opens the door to better design of coupling architectures to create the desired type of stable oscillations. We then use coupling that is both amplitude and phase dependent to create either globally stable synchronous or traveling-wave solutions. Using the CPG motor neuron network of a leech as an example, we show that while both traveling and synchronous oscillations can be achieved by several types of coupling, the transition between different types of behavior is dictated by a specific coupling architecture. In particular, it is only the “repulsive” but not the commonly used phase or rotational coupling that can explain the transition to high-frequency synchronous oscillations that have been observed in the heartbeat pattern generator of a leech. This shows that the overall dynamics of a CPG can be highly sensitive to the type of coupling used, even for coupling architectures that are widely believed to produce the same qualitative behavior. |
| first_indexed | 2024-09-23T17:03:36Z |
| format | Article |
| id | mit-1721.1/76203 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T17:03:36Z |
| publishDate | 2013 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/762032022-09-29T23:23:43Z Control of traveling-wave oscillations and bifurcation behavior in central pattern generators Landsman, Alexandra S. Slotine, Jean-Jacques E. Massachusetts Institute of Technology. Department of Mechanical Engineering Slotine, Jean-Jacques E. Understanding synchronous and traveling-wave oscillations, particularly as they relate to transitions between different types of behavior, is a central problem in modeling biological systems. Here, we address this problem in the context of central pattern generators (CPGs). We use contraction theory to establish the global stability of a traveling-wave or synchronous oscillation, determined by the type of coupling. This opens the door to better design of coupling architectures to create the desired type of stable oscillations. We then use coupling that is both amplitude and phase dependent to create either globally stable synchronous or traveling-wave solutions. Using the CPG motor neuron network of a leech as an example, we show that while both traveling and synchronous oscillations can be achieved by several types of coupling, the transition between different types of behavior is dictated by a specific coupling architecture. In particular, it is only the “repulsive” but not the commonly used phase or rotational coupling that can explain the transition to high-frequency synchronous oscillations that have been observed in the heartbeat pattern generator of a leech. This shows that the overall dynamics of a CPG can be highly sensitive to the type of coupling used, even for coupling architectures that are widely believed to produce the same qualitative behavior. 2013-01-08T17:50:55Z 2013-01-08T17:50:55Z 2012-10 2012-05 Article http://purl.org/eprint/type/JournalArticle 1539-3755 1550-2376 http://hdl.handle.net/1721.1/76203 Landsman, Alexandra, and Jean-Jacques Slotine. “Control of Traveling-wave Oscillations and Bifurcation Behavior in Central Pattern Generators.” Physical Review E 86.4 (2012). © 2012 American Physical Society https://orcid.org/0000-0002-7161-7812 en_US http://dx.doi.org/10.1103/PhysRevE.86.041914 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Landsman, Alexandra S. Slotine, Jean-Jacques E. Control of traveling-wave oscillations and bifurcation behavior in central pattern generators |
| title | Control of traveling-wave oscillations and bifurcation behavior in central pattern generators |
| title_full | Control of traveling-wave oscillations and bifurcation behavior in central pattern generators |
| title_fullStr | Control of traveling-wave oscillations and bifurcation behavior in central pattern generators |
| title_full_unstemmed | Control of traveling-wave oscillations and bifurcation behavior in central pattern generators |
| title_short | Control of traveling-wave oscillations and bifurcation behavior in central pattern generators |
| title_sort | control of traveling wave oscillations and bifurcation behavior in central pattern generators |
| url | http://hdl.handle.net/1721.1/76203 https://orcid.org/0000-0002-7161-7812 |
| work_keys_str_mv | AT landsmanalexandras controloftravelingwaveoscillationsandbifurcationbehaviorincentralpatterngenerators AT slotinejeanjacquese controloftravelingwaveoscillationsandbifurcationbehaviorincentralpatterngenerators |