Stability Analysis of Delayed Age-structured Resource-Consumer Model of Population Dynamics with Saturated Intake Rate

The nonlinear n-resource-consumer autonomous system with age-structured consumer population is studied. While the model of consumer population dynamics is described by a delayed transport equation, the dynamics of resource patches are described by ordinary differential equations with saturated intake rate. The delay models the digestion period of generalist consumer and is included in the calorie intake rate which impacts on consumer’s fertility and mortality. Saturated intake rate models the inhibition effect from the behavioural change of the resource patches when they react on the consumer population growing or from the crowding effect of the consumer. The model is studied both analytically and numerically. Conditions for existence of trivial, semi-trivial and non-trivial equilibria and their local asymptotic stability are obtained. Numerical experiments confirm and illustrate these theoretical results.