Study of Increasing Population and their Sensitivity Analysis with Second Order Differential Equations
Keywords:
Single-species, Second-order differential equation model, stochastic stability, intraspecific interaction, age distribution, population model, living organism.Abstract
Models of populations are helpful tools for investigating populations in which intraspecific interactions account for the vast bulk of the variation in the population dynamics. These models are predicated on the assumption that we can learn about a species' dynamics simply by observing it. The growth dynamics of a homogeneous population is often described using first-order differential equations (both linear and nonlinear). Second, the paper attempts to develop a second-order differential equation model of single-species population growth that is consistent with Newtonian mechanics, and third, it attempts to investigate the stochastic stability of the population system to consider environmental fluctuation in the system. In this study, we provide a second-order differential equation model of a single species' population expansion that is consistent with Newtonian physics and evolutionary theory. Clark tested the validity of this hypothesis by collecting observational data from the bighorn sheep and mule deer populations in the American West and Southwest. As a result of the stochastic stability of the deterministic model, it is more probable that the model will be right even when the random environment changes somewhat.
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https://hankstevens.github.io/Primer-of-Ecology/DDgrowth.html#continuous-logistic-growth
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