{"id":{"repo_id":"uvic","oai_identifier":"oai:dspace.library.uvic.ca:1828/18185"},"canonical_url":"https://search.dev.ndltd.org/etd/uvic/oai:dspace.library.uvic.ca:1828/18185","repository":{"repo_id":"uvic","name":"University of Victoria (Canada)","base_url":"https://dspace.library.uvic.ca/server/oai/request"},"display":{"title":"Modeling central pattern generators in sand crabs","abstract":"Ordinary differential equation models based on those of Hodgkin and Huxley are pre­sented in an effort to describe a part icular anomalous digging behaviour in t he anomuran decapod crust acean Emerita analoga. At the onset of a dig, the fourth (hindmost) right and left legs stroke together about half a cycle out of phase wit h the uropods (last ab­dominal appendages). During digging, however , the phase relationships between the fourth legs and uropods change and one leg ( either left or right) begins to lead the other. Two general approaches are taken here to model the central pattern generators (CP Gs) that coordinate each appendage, and these CPG models are coupled together in order to de­scribe the full network. First, CPGs comprise cells, or small groups of cells described by Morris-Lecar equations. Simply coupling these cellular models together results in high di­mensional systems of ordinary differential equations that can only be analysed numerically except in special symmetric cases. However , using similar equations to model each CPG permits averaging which reduces t he \"important\" dimension of t he system to three , namely a single phase variable for each appendage . So t he second approach taken here is to model each CPG as a single oscillator coupled to others by a phase response function, computed numerically from the cellular differential equations. The resulting three dimensional system is much easier to analyse and it is used to show that with minimal sensory input , a neural network consisting of three coupled oscillators i sufficient to account for the anomalous digging behaviour in Emerita.","abstract_html":"Ordinary differential equation models based on those of Hodgkin and Huxley are pre­sented in an effort to describe a part icular anomalous digging behaviour in t he anomuran decapod crust acean Emerita analoga. At the onset of a dig, the fourth (hindmost) right and left legs stroke together about half a cycle out of phase wit h the uropods (last ab­dominal appendages). During digging, however , the phase relationships between the fourth legs and uropods change and one leg ( either left or right) begins to lead the other. Two general approaches are taken here to model the central pattern generators (CP Gs) that coordinate each appendage, and these CPG models are coupled together in order to de­scribe the full network. First, CPGs comprise cells, or small groups of cells described by Morris-Lecar equations. Simply coupling these cellular models together results in high di­mensional systems of ordinary differential equations that can only be analysed numerically except in special symmetric cases. However , using similar equations to model each CPG permits averaging which reduces t he "important" dimension of t he system to three , namely a single phase variable for each appendage . So t he second approach taken here is to model each CPG as a single oscillator coupled to others by a phase response function, computed numerically from the cellular differential equations. The resulting three dimensional system is much easier to analyse and it is used to show that with minimal sensory input , a neural network consisting of three coupled oscillators i sufficient to account for the anomalous digging behaviour in Emerita.","abstract_has_math":false,"creators":["Hodge, Alexander Fraser Cooper"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003","date_published":"2003","updated_at":"2026-07-24T05:52:40Z","subjects":[],"languages":[],"rights":["Available to the World Wide Web"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1828/18185","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Hodge, Alexander Fraser Cooper"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-08-14T17:18:12Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-08-14T17:18:12Z"]},{"key":"dc:date.issued","label":"Date","values":["2003"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Available to the World Wide Web"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1828/18185"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Ordinary differential equation models based on those of Hodgkin and Huxley are pre­sented in an effort to describe a part icular anomalous digging behaviour in t he anomuran decapod crust acean Emerita analoga. At the onset of a dig, the fourth (hindmost) right and left legs stroke together about half a cycle out of phase wit h the uropods (last ab­dominal appendages). During digging, however , the phase relationships between the fourth legs and uropods change and one leg ( either left or right) begins to lead the other. Two general approaches are taken here to model the central pattern generators (CP Gs) that coordinate each appendage, and these CPG models are coupled together in order to de­scribe the full network. First, CPGs comprise cells, or small groups of cells described by Morris-Lecar equations. Simply coupling these cellular models together results in high di­mensional systems of ordinary differential equations that can only be analysed numerically except in special symmetric cases. However , using similar equations to model each CPG permits averaging which reduces t he \"important\" dimension of t he system to three , namely a single phase variable for each appendage . So t he second approach taken here is to model each CPG as a single oscillator coupled to others by a phase response function, computed numerically from the cellular differential equations. The resulting three dimensional system is much easier to analyse and it is used to show that with minimal sensory input , a neural network consisting of three coupled oscillators i sufficient to account for the anomalous digging behaviour in Emerita."]},{"key":"dc:title","label":"Title","values":["Modeling central pattern generators in sand crabs"]}]}],"canonical_facts":{"dc:creator":["Hodge, Alexander Fraser Cooper"],"dc:date.accessioned":["2024-08-14T17:18:12Z"],"dc:date.available":["2024-08-14T17:18:12Z"],"dc:date.issued":["2003"],"dc:description.abstract":["Ordinary differential equation models based on those of Hodgkin and Huxley are pre­sented in an effort to describe a part icular anomalous digging behaviour in t he anomuran decapod crust acean Emerita analoga. At the onset of a dig, the fourth (hindmost) right and left legs stroke together about half a cycle out of phase wit h the uropods (last ab­dominal appendages). During digging, however , the phase relationships between the fourth legs and uropods change and one leg ( either left or right) begins to lead the other. Two general approaches are taken here to model the central pattern generators (CP Gs) that coordinate each appendage, and these CPG models are coupled together in order to de­scribe the full network. First, CPGs comprise cells, or small groups of cells described by Morris-Lecar equations. Simply coupling these cellular models together results in high di­mensional systems of ordinary differential equations that can only be analysed numerically except in special symmetric cases. However , using similar equations to model each CPG permits averaging which reduces t he \"important\" dimension of t he system to three , namely a single phase variable for each appendage . So t he second approach taken here is to model each CPG as a single oscillator coupled to others by a phase response function, computed numerically from the cellular differential equations. The resulting three dimensional system is much easier to analyse and it is used to show that with minimal sensory input , a neural network consisting of three coupled oscillators i sufficient to account for the anomalous digging behaviour in Emerita."],"dc:identifier.uri":["https://hdl.handle.net/1828/18185"],"dc:rights":["Available to the World Wide Web"],"dc:title":["Modeling central pattern generators in sand crabs"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T05:52:40Z"}