Abstract
We consider a predator-prey relationship in a fair system in which interacting species have different needs of resources to survive. We analyzed qualitatively the outcome of interaction using a modified logistic predator-prey model with Allee threshold in both predator and prey equations. We showed that the system had very rich dynamical behavior as stability around fixed points and periodic solutions could be obtained at certain conditions. Interaction outcome is highly submitted to initial conditions, species behavior, and the threshold applied. Numerical results suggested adapting resource allocation and the threshold value to optimize ecosystem sustainability.
Highlights
In an ecosystem where resource accessibility for interactive species is fair, competition intensity, which can be assimilated to each species ability to harvest, is a key parameter in controlling system stability and optimizing ecosystem sustainability
Classical Lotka–Volterra systems by supposing unlimited resources for interacting species and focusing mainly on interaction outcome fail to formalize small variations happening in species intrinsic growth rate due to resource abundance, competition, or delay in assimilation of harvested resource, for example
Models with Allee-threshold extinction control mechanism present the advantage of capturing such variations of species growth rate by setting a maximum value to reach for population size to not go extinct [10–15]
Summary
In an ecosystem where resource accessibility for interactive species is fair, competition intensity, which can be assimilated to each species ability to harvest, is a key parameter in controlling system stability and optimizing ecosystem sustainability. We are interested in analyzing an ecosystem with limited resources in which two interacting species with different needs and resource accessibility are competing for their growth and survival We assimilate this type of dynamic and relationship to online social network users characterized by their traffic profile during peak hours. Predator-prey principle formalizes variation over time of population density due to the presence or absence of other species in the ecosystem, representing the effect of increase or decrease via interaction coefficients. Based on this principle, U1 and U2 amount of packets traveling the segment will vary in function of interaction intensity and overall U1 or U2 amount of packets queuing at the buffer space. Coefficient A is the threshold setup to control extinction of species. is parameter has to be fixed smaller than segment maximum carrying capacity such that, at any t > 0, users’ generated amount of packets never exceed this value
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