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A nonlinear model of age and maturity structured population dynamics is analyzed. The population is structured by age and maturity of the individuals and the nonlinearity in the equations corresponds to density dependent limitation of population growth. The existence and asymptotic behavior of solutions are studied.

Instability, hypercyclicity and chaos are investigated in a nonlinear model of age and maturity structured population dynamics. It is demonstrated that the behavior of solutions depends on the viewpoint of the observer. Viewed in the direction of age structure the population stabilizes to a regular distribution. Viewed in the direction of maturity structure there is the possibility of chaotic behavior.

An analysis of a model of tumor growth into surrounding tissue is continued from an earlier treatment, in which the global existence of unique solutions to the model was established. The model consists of a system of nonlinear partial differential equations for the population densities of tumor cells, extracellular matrix macromolecules, oxygen concentration, and extracellular matrix degradative enzyme concentration. The spatial growth of the tumor involves the directed movement of tumor cells toward the extracellular matrix through haptotaxis. Cell age is used to track progression of cells through the cell cycle. Regularity, positivity, and global bounds of the solutions of the model are proved.analytic semigroup, cell proliferation, degradation enzyme, diffusion, extracellular matrix, fractional power, haptotaxis, tumor cells,