ABSTRACT
This chapter considers several "vectors" of such efforts, which make use of the previous findings in stability analysis applied to the new models. The constant schedule of the organism's life span, which is one of the principal limitations of the Leslie formalism, often contradicts the variability observed in nature or in experiments. The "challenge to linear algebra" resulted in an exhaustive description of the asymptotics inherent in the classical Leslie model. Another kind of limitation of the Leslie model, when used to simulate dynamics of real populations, is related to the pattern of trajectory behavior in general and the period of cycles in particular. Typical for many populations, the cycles can somehow be mimicked in a Leslie model only if their period does not exceed the life span of the organisms. The classical Leslie model presupposes the birth and survival rates to be constant, irrespective of what is the current population density.
