Dissertation > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations

The Study of Modeling Differential Equations in a One-Dimensional Network of Theta Neurons

Author GaoFeiFei
Tutor HaoDunYuan
School Inner Mongolia University
Course Applied Mathematics
Keywords theta model traveling wave solution synaptic coupling shooting method perturbation
CLC O175
Type Master's thesis
Year 2006
Downloads 30
Quotes 1
Download Dissertation

This paper focuses on the modeling differential equations in a one-dimensional network of theta neurons. The problem is studied from two aspects: the physiological movement characteristics of neurons and the modeling differential equations. At first, we simplify the computational models for synaptically coupled networks of neurons in order to obtain the regular traveling waves in a one-dimensional network of theta neurons. Then we set assumption on the form of input. Thus, we can show, in a different way, that for any wave speed, there exists a coupling strength such that there exists one traveling wave solution for this network. Moreover, we proved that under small extra perturbation, there exists two traveling wave solutions which spike more than one time.

Related Dissertations
More Dissertations