Date of Graduation
Master of Science in Mathematics
Population modeling, Lotka - Volterra models, alpha-functions, conditional interactions, stability, bifurcations
Based on observations that at different points in time, the biological interaction between two species can vary, four two-species models which allow for variable interspecies interactions are studied. The interaction models are modified Lotka-Volterra equations where the association between the two species is modeled by piecewise linear α-functions. An analysis of stability properties and number of equilibrium points is carried out for each model, and the type of interaction that each equilibrium point represents is determined. The non-existence of biologically relevant periodic solutions is established as well as the existence of bifurcation phenomena. Specifically, the existence of two transcritical and one Hopf bifurcation is established using both graphical and analytical methods.
© Katharina Voelkel
Voelkel, Katharina, "Dynamics and Bifurcations in Variable Biological Two Species Interaction Models Implementing Piecewise Linear Alpha-Functions" (2012). MSU Graduate Theses. 1641.