Abstract
We present a density-dependent population dynamics model with age-dependence, child care, and spatial dispersal. The population consists of the young (under maternal care), juvenile, and adult (producing offsprings at fixed ages or of post-reproductive age) classes. Death moduli of the juvenile and adult individuals are decomposed into two-term sums. The first sum represents the death rate by natural causes and by those that do not depend on the population spatial density, while the other one describes the environmental influence depending on the spatial density of the juvenile and adult individuals. The steady-state and a class of separable solutions are considered, and the large-time behavior of separable solutions is analyzed for the stationary vital rates. The asymptotic behavior of nondispersing semelparous species is also examined.
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