English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We derive an alternative expression for a delayed logistic equation in whichthe rate of change in the population involves a growth rate that depends on thepopulation density during an earlier time period. In our formulation, the delayin the growth term is consistent with the rate of instantaneous decline in thepopulation given by the model. Our formulation is a modification of [Arino etal., J.~Theoret.~Biol.~241(1):109--119, 2006] by taking the intraspecificcompetition between the adults and juveniles into account. We provide acomplete global analysis showing that no sustained oscillations are possible. Athreshold giving the interface between extinction and survival is determined interms of the parameters in the model. The theory of chain transitive sets andthe comparison theorem for cooperative delay differential equations are used todetermine the global dynamics of the model.  We extend our delayed logistic equation to a system modeling the competitionof two species. For the competition model, we provide results on localstability, bifurcation diagrams, and adaptive dynamics. Assuming that thespecies with shorter delay produces fewer offspring at a time than the specieswith longer delay, we show that there is a critical value, $\tau^*$, such thatthe evolutionary trend is for the delay to approach $\tau^*$.

Population Growth and Competition Models with Decay and Competition Consistent Delay