caa a22 4500 445330430 CHVBK 20180317142735.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00285-010-0348-6 doi (NATIONALLICENCE)springer-10.1007/s00285-010-0348-6 Entrainment ranges of forced phase oscillators [Elektronische Daten] [Joseph Previte, Natalie Sheils, Kathleen Hoffman, Tim Kiemel, Eric Tytell] In the vertebrate spinal cord, a neural circuit called the central pattern generator produces the basic locomotory rhythm. Short and long distance intersegmental connections serve to maintain coordination along the length of the body. As a way of examining the influence of such connections, we consider a model of a chain of coupled phase oscillators in which one oscillator receives a periodic forcing stimulus. For a certain range of forcing frequencies, the chain will match the stimulus frequency, a phenomenon called entrainment. Motivated by recent experiments in lampreys, we derive analytical expressions for the range of forcing frequencies that entrain the chain, and how that range depends on the forcing location. For short intersegmental connections, in which an oscillator is connected only to its nearest neighbors, we describe two ways in which entrainment is lost: internally, in which oscillators within the chain no longer oscillate at the same frequency; and externally, in which the the chain no longer has the same frequency as the forcing. By analyzing chains in which every oscillator is connected to every other oscillator (i.e., all-to-all connections), we show that the presence of connections with lengths greater than one do not necessarily change the entrainment ranges based on the nearest-neighbor model. We derive a criterion for the ratio of connection strengths under which the connections of length greater than one do not change the entrainment ranges produced in the nearest-neighbor model, provided entrainment is lost externally. However, when this criterion holds, the range of entrained frequencies is a monotonic function of forcing location, unlike experimental results, in which entrainment ranges are larger near the middle of the chain than at the ends. Numerically, we show that similar non-monotonic entrainment ranges are possible if the ratio criterion does not hold, suggesting that in the lamprey central pattern generator, intersegmental connection strengths are not a simple function of the connection length. Springer-Verlag, 2010 Entrainment ranges nationallicence Coupled oscillators nationallicence Locomotion nationallicence Central pattern generator nationallicence Previte Joseph School of Science, Penn State Erie, The Behrend College, Erie, PA, USA aut Sheils Natalie Department of Mathematics, Seattle University, Seattle, WA, USA aut Hoffman Kathleen Department of Mathematics and Statistics, UMBC, Baltimore, MD, USA aut Kiemel Tim Department of Kinesiology, University of Maryland, College Park, MD, USA aut Tytell Eric Department of Biology and Institute for Systems Research, University of Maryland, College Park, MD, USA aut Journal of Mathematical Biology Springer-Verlag 62/4(2011-04-01), 589-603 0303-6812 62:4<589 2011 62 285 https://doi.org/10.1007/s00285-010-0348-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0348-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Previte Joseph School of Science, Penn State Erie, The Behrend College, Erie, PA, USA aut NATIONALLICENCE 700 1- Sheils Natalie Department of Mathematics, Seattle University, Seattle, WA, USA aut NATIONALLICENCE 700 1- Hoffman Kathleen Department of Mathematics and Statistics, UMBC, Baltimore, MD, USA aut NATIONALLICENCE 700 1- Kiemel Tim Department of Kinesiology, University of Maryland, College Park, MD, USA aut NATIONALLICENCE 700 1- Tytell Eric Department of Biology and Institute for Systems Research, University of Maryland, College Park, MD, USA aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 62/4(2011-04-01), 589-603 0303-6812 62:4<589 2011 62 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer