Studies of a mathematical model for generating rhythmic behavior with a simple brain

Authors

Juan C. Morales, University of Texas-Pan American

Date of Award

7-2014

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Virgil Pierce

Second Advisor

Dr. Daniel Plas

Third Advisor

Dr. Maria Cristina Villalobos

Abstract

The rhythmic behavior of feeding in the pond snail, Lymnaea stagnalis can be described computationally by a model describing its central pattern generator network (CPG). The model includes coupled Hodgkin-Huxley type nonlinear ordinary differential equations describing four neurons connected by both inhibitory and excitatory synapses. We studied the system’s dependence on current parameters to generate periodic behavior. We also considered the effect of eliminating specific connections from the network. In addition, experiments on the biological system were used to motivate application of the model in Parkinson’s disease.

Comments

Copyright 2014 Juan C. Morales. All Rights Reserved.

https://www.proquest.com/dissertations-theses/studies-mathematical-model-generating-rhythmic/docview/1572056228/se-2

Granting Institution

University of Texas-Pan American