Asymptotic stability of delayed consumer age-structured population models with an Allee effect

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

“…Equations (7), (8) means that decreasing of calorie intake rate corresponds to the critical foraging or starvation, and increasing of it corresponds to the sufficient foraging and satiation with increasing resource intake rate. Increasing of calorie intake rate provides also maximum comfortable conditions for reproduction of consumers that corresponds to increasing of birth rate, and decreasing of calorie intake rate provides the most poor and unfavourable conditions for reproduction of consumers, decreasing of birth rate.…”

“…The basic reproduction number of age-structured model of consumer population dynamics [8], [16], [28], [35], [41] is a calorie intake rate depending function:…”

“…and coefficients of system (1) -(5) satisfy Eqs. (7), (8). Then, for existence of at least one non-trivial solution of stationary problem (11), (12), (18) -equilibrium * * ( ) ( , )…”

“…In traditional unstructured Lotka-Volterra ODE models of population dynamics, many details of life histories are neglected [16]. The more reasonable approach in population dynamics modelling is based on the physiologically structured models [8], [11], [13], [14], [16] - [21], [28], [29], [35], [36], [41], [42]. In this article the apparent competition model of unstructured resource patches with age-structured consumer population is studied.…”

“…The local asymptotic stability of all equilibria is considered in Section 4. Stability analysis is based on the traditional perturbation theory and linearization of autonomous system and includes the study of impact of the time delay parameter on the asymptotic stability of equilibria [3], [8], [19], [36], [38], [39].…”