| Title |
An Alternative Formulation for a Distributed Delayed Logistic Equation
|
|---|---|
| Published in |
Bulletin of Mathematical Biology, April 2018
|
| DOI | 10.1007/s11538-018-0432-4 |
| Pubmed ID | |
| Authors |
Chiu-Ju Lin, Lin Wang, Gail S. K. Wolkowicz |
| Abstract |
We study an alternative single species logistic distributed delay differential equation (DDE) with decay-consistent delay in growth. Population oscillation is rarely observed in nature, in contrast to the outcomes of the classical logistic DDE. In the alternative discrete delay model proposed by Arino et al. (J Theor Biol 241(1):109-119, 2006), oscillatory behavior is excluded. This study adapts their idea of the decay-consistent delay and generalizes their model. We establish a threshold for survival and extinction: In the former case, it is confirmed using Lyapunov functionals that the population approaches the delay modified carrying capacity; in the later case the extinction is proved by the fluctuation lemma. We further use adaptive dynamics to conclude that the evolutionary trend is to make the mean delay in growth as short as possible. This confirms Hutchinson's conjecture (Hutchinson in Ann N Y Acad Sci 50(4):221-246, 1948) and fits biological evidence. |
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| Country | Count | As % |
|---|---|---|
| Unknown | 2 | 100% |
Demographic breakdown
| Type | Count | As % |
|---|---|---|
| Scientists | 1 | 50% |
| Members of the public | 1 | 50% |
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| Country | Count | As % |
|---|---|---|
| Unknown | 8 | 100% |
Demographic breakdown
| Readers by professional status | Count | As % |
|---|---|---|
| Student > Ph. D. Student | 2 | 25% |
| Researcher | 2 | 25% |
| Unknown | 4 | 50% |
| Readers by discipline | Count | As % |
|---|---|---|
| Mathematics | 2 | 25% |
| Agricultural and Biological Sciences | 1 | 13% |
| Sports and Recreations | 1 | 13% |
| Unknown | 4 | 50% |
Attention Score in Context
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