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Some Remarks on a Non-Local Variable Carrying Capacity Model for Aphid Population Dynamics
- Publication Year :
- 2023
-
Abstract
- Aphids are damaging insect pests on many crops. Their density can rapidly build up on a host plant to several thousand over one growing season. Occasionally, a competition-driven decline in population early in the season, followed by a build-up later, is observed in the field. Such dynamics cannot be captured via standard models, such as introduced in Kindlmann and Dixon, 2010. In Kindlmann et al., 2007, a logistic non-local population model with variable carrying capacity is proposed to capture these alternative dynamics. The proposed model has a rich dynamical structure and can predict multiple population peaks, as observed in the field. We show that additionally, this model also possesses solutions that can blow-up/explode in finite time. The blow-up is seen to occur for both large and small initial conditions and can occur both early and late in the season. We propose a model extension that, under certain parametric restrictions, has global time-bounded solutions. We discuss the ecological applications of our findings.<br />Comment: 21 pages, 8 figures
- Subjects :
- Quantitative Biology - Populations and Evolution
Mathematics - Dynamical Systems
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2310.03058
- Document Type :
- Working Paper