Stability Analysis of Delayed Age-structured Resource-Consumer Model of Population Dynamics with Saturated Intake Rate
| Autor: | V. V. Akimenko |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
age-structured model
Resource (biology) Intake rate digestion period Population lcsh:Evolution Metapopulation Generalist and specialist species stability analysis Stability (probability) Exponential stability lcsh:QH540-549.5 Econometrics lcsh:QH359-425 Applied mathematics Quantitative Biology::Populations and Evolution Growth rate Uniqueness education Ecology Evolution Behavior and Systematics Mathematics education.field_of_study Smoothness (probability theory) Ecology saturated intake rate Optimal control Nonlinear system Ordinary differential equation lcsh:Ecology resource-consumer model |
| Zdroj: | Frontiers in Ecology and Evolution, Vol 9 (2021) |
| DOI: | 10.1101/2020.01.10.901629 |
| Popis: | This article studies nonlinear n-resource-consumer autonomous system with age-structured consumer population. The model of consumer population dynamics is described by a delayed transport equation, and 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 the consumer’s fertility and mortality. Saturated intake rate models the inhibition effect from the behavioral change of the resource patches when they react to the consumer population growing or from the crowding effect of the consumer. The conditions for the existence of trivial, semi-trivial, and non-trivial equilibria and their local asymptotic stability were obtained. The local asymptotic stability/instability of non-trivial equilibrium of a 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. The digestion period of a 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 the study of metapopulation dynamics, desert locust populations dynamics, prey-predator interactions in fisheries, etc. The paper uses numerical experiments to confirm and illustrate all dynamical regimes of the n-resource-consumer population. |
| Databáze: | OpenAIRE |
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