Abstract:

The article is concerned with the existence of positive equilibria and stability of zero state in a nonlinear hierarchical species. Based on the assumption that young individuals are more competitive than older ones, an integro-partial differential equation is taken to model the revolution process of the population. The net reproductive number is defined and used to show that there are positive steady states in the system. Furthermore, stability results for zero equilibrium are derived via the characteristic equation and a Liapunov function. Finally, some numerical experiments are presented.

Key words: Hierarchy of ages, Positive equilibria, Stability, Non-zero fixed points