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

Autor: Vlastimil Křivan, V. V. Akimenko
Rok vydání: 2018
Předmět:
Male
0106 biological sciences
0301 basic medicine
Statistics and Probability
Population Dynamics
Population
Models
Biological
010603 evolutionary biology
01 natural sciences
General Biochemistry
Genetics and Molecular Biology
03 medical and health sciences
symbols.namesake
Exponential stability
Stability theory
Animals
Quantitative Biology::Populations and Evolution
Applied mathematics
Computer Simulation
Mortality
Birth Rate
education
Mathematics
Allee effect
Population Density
education.field_of_study
Extinction
General Immunology and Microbiology
Applied Mathematics
Mathematical Concepts
General Medicine
030104 developmental biology
Density dependence
Nonlinear Dynamics
Population model
Modeling and Simulation
symbols
Female
General Agricultural and Biological Sciences
Basic reproduction number
Zdroj: Mathematical Biosciences. 306:170-179
ISSN: 0025-5564
DOI: 10.1016/j.mbs.2018.10.001
Popis: In this article we study a nonlinear age-structured consumer population model with density-dependent death and fertility rates, and time delays that model incubation/gestation period. Density dependence we consider combines both positive effects at low population numbers (i.e., the Allee effect) and negative effects at high population numbers due to intra-specific competition of consumers. The positive density-dependence is either due to an increase in the birth rate, or due to a decrease in the mortality rate at low population numbers. We prove that similarly to unstructured models, the Allee effect leads to model multi-stability where, besides the locally stable extinction equilibrium, there are up to two positive equilibria. Calculating derivatives of the basic reproduction number at the equilibria we prove that the upper of the two non-trivial equilibria (when it exists) is locally asymptotically stable independently of the time delay. The smaller of the two equilibria is always unstable. Using numerical simulations we analyze topologically nonequivalent phase portraits of the model.
Databáze: OpenAIRE
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