An investigation of a resource-consumer system by using continuous system modeling program and stability analysis

This thesis presents two resource-consumer systems, one based upon the classical Gallopin model and another based upon the classical Gallopin model combined with the Smith's hypothesis. The models are studied via numerical and analytical techniques. The Continuous System Modeling Program is used to study the effect of parameters on the response of these two systems. The analytical approach used in the stability analysis consists of linearization combined with the Hurwitz stability criterion.

Necessary and sufficient conditions for local stability for both the extended Gallopin and Smith systems are found. In general, more restrictions are needed to guarantee stability in the extended Smith system than are necessary for the extended Gallopin model. From the computer output, a similar result is obtained. More damping and restrictions on parameters are observed.