TOPICS IN MATHEMATICAL BIOLOGY

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Our research efforts will center on the use of a variety of mathematical techniques to solve and analyze the complex difference and differential equations that arise in the modeling of systems in biology, ecology and physiology. Particular systems of interest include: * periodic diseases * the renal concentrating mechanism * biochemical oscillators * reaction-advection processes * long-term fluctuations of populations * nonlinear models of the DNA molecule * drug distribution (compartmental models) Exact, approximate and numerical solutions will be obtained. The mathematical techniques to be used include perturbation (both regular and singular) and asymptotic series, harmonic balance procedures, phase-space analysis, the 'theory' of chaotic systems, and numerical integration.