Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 260, Issue 2, Pages 1918-1953Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2015.09.048
Keywords
Competition; Stage structure; Delay; Monotone system; Exponential ordering
Categories
Funding
- Leverhulme Trust [RF-2014-512]
- National Natural Science Foundation of China [11371111]
- Fundamental Research Funds for the Central Universities of China [AUGA5710050313]
- NSFC [11301442]
- RGC [PolyU 253004/14P]
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In some species, larvae and adults experience competition in completely different ways. Simple stage structured models without larval competition usually yield a single delay equation for the adults. Using an age structured system incorporating competition among both larvae and adults, we derive a system of distributed delay equations for the numbers of larvae and adults. The system is neither cooperative nor reducible to a single equation for either variable. Positivity, boundedness and uniform strong persistence are established. Linear stability analysis of equilibria is difficult due to the strong coupling, but results are proved for small delays using monotone systems theory and exponential ordering. For small delay we prove a theorem on generic convergence to equilibria, which does not directly follow from standard theory but can be proved indirectly using comparison arguments. Finally, we consider an extension to two-strain competition and prove theorems on the linear stability of the boundary equilibria. (C) 2015 Elsevier Inc. All rights reserved.
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