9404604 Rivera The investigator extends a variety of theoretical results for dynamical systems and applies them to problems in electrical engineering and mathematical biology. The theoretical results include: shooting methods, spectral analysis of operators on Banach spaces to obtain new results on invariant manifolds, and linearizations about stationary solutions. These results are applied to analyse the existence and stability of travelling waves in PDE epidemic models and the losses in NFDE models of electrical power transmission lines. Biologists have observed that animal and human epidemics spread throughout a geographical area in the form of a travelling wave. Engineers have observed how much loss occurs as electricityis transmitted through power lines over distances. The mathematical models mentioned above give reasonable approximations to essential features of these physical phenomena and enable us to improve our ability to predict and control them. This is important because of the expanding problem of animal and human epidemics (e.g. HIV-AIDS and rabies). The investigator applies analytical and computational methods to improve understanding of these models and to interpret the physical meaning of the results.
