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A comparative study of stability conditions in dynamical systems, cobweb models, and differential delay equations

University of British Columbia

In the study of ordinary differential equations (ODE), a wealth of time has been spent studying dynamical systems. Because of this, much is known about the behaviour of such systems and many methods have been developed to further aid in their analysis. Through comparisons and the construction of actual parallels, this thesis attempts to show how this knowledge of dynamical systems can also be useful in the study of cobweb models and differential delay equations (DDE). Concentration is placed on the development of methods for stability analysis, with general introductions to stability analysis in dynamical systems, cobweb models and differential delay systems. A special parallel is drawn between Hopf-type bifurcation in dynamical systems and Ailwright bifurcation in cobweb models; while the construction of equivalent dynamical systems for S-convertible DDE is presented and stability analysis is carried out for several special examples.

Text

2010-07-17

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http://hdl.handle.net/2429/26583

Mathematics

University of British Columbia

Graduate