Qualitative Analysis of a Model of Renewable Resources and Population with Distributed Delays

Abstract

This work generalizes Matsumoto et al.’s dynamic model of population and renewable resources by substituting a distributed delay for the time delay. It is proved that the equilibrium point may lose or gain local stability, allowing for the observation of alternating stability/instability areas if some conditions hold.

Keywords

• distributed delay
• Easter Island
• Hopf bifurcation