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Global exponential stability analysis for tick population model with delayed sub-linear Gamma-Ricker nonlinearities.
- Source :
-
Journal of Differential Equations . May2023, Vol. 355, p369-385. 17p. - Publication Year :
- 2023
-
Abstract
- We argue that self-regulation in tick population dynamics in the natural world is not associated with the egg-production saturation, that was normally assumed in existing literature and modeled using the Ricker reproduction function. We argue that the nonlinearity and self-regulatory inhibition appear in the synergistic effect of tick cooperation and the crowding within groups, and an appropriate nonlinearity can be the sub-linear Gamma-Ricker function. We also noticed that the diapaused development leads to multiple time lags in a structured tick population dynamics model, leading to a scalar delay differential equation with two time lags appearing in the sub-linear Gamma-Ricker nonlinearity. This model has always one and only one positive equilibrium. Here we develop sharp conditions for this model to exhibit persistence and global convergence behaviors. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 355
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 162475077
- Full Text :
- https://doi.org/10.1016/j.jde.2022.12.025