Stability Analysis of Delayed Age-Structured Resource-Consumer Model of Population Dynamics With Saturated Intake Rate - Akimenko, Vitalii V. (Frontiers in Ecology and Evolution, 2021)
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 ODE 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 behavioral change of the resource patches when they react on the consumer population growing or from the crowding effect of the consumer. Conditions for existence of trivial, semi-trivial and nontrivial equilibria and their local asymptotic stability are obtained. Local asymptotic stability/instability of non-trivial equilibrium of system with depleted patches is defined by new derived criteria which relate the demographic characteristics of consumers with their search rate, growth rate of resource in patches and behavioral change of the food resource when consumer population grows. Digestion period of generalist consumer does not cause local asymptotical instabilities of consumer population at the semi-trivial and nontrivial equilibria. These theoretical results may be used in study of metapopulation dynamics, desert locust populations dynamics, prey-predator interactions in fisheries, etc. Numerical experiments confirm and illustrate all dynamical regimes of n-resource-consumer population obtained in paper.