Abstract
In the recent decades, biology and ecology area and also computer and network sciences are marched on at a rapid pace toward perfection by help of mathematical concepts such as stability, bifurcation, chaos and etc. Because of no existing any interspecific interaction in the single species, one is able to see that this is the simplest model. Meanwhile by adding some assumptions, we see that it has so many practical applications in the nature and any branch of sciences. In this article, some dynamical models of single species are studied. First, Picard's iteration method for exponential growth rate is analyzed. In continuation, some logistic models for both cases without harvesting and having harvested factor which are constant or variable are studied. Indeed, the solution and stability of equilibria for the said models are analyzed. Finally, in the section of simulation analysis by help of \textit{mathlab software}, we give some numerical simulations to support of our mathematical conclusions which show the stability of the equilibria for I.V.Ps. of the logistic equation developed.
Highlights
Population ecologists use methods to model the population dynamics
Anybody knows the importance and effect of single species in community and nature, and so we present a summary and brief literature of mathematical models such as single species, exponential and logistic modeling used to describe population dynamics, which may help us future model development and highlights the importance of population growth rate modeling in biology, ecology, and another area even computer and network sciences
Anybody gets involved with microbe viruses and such as Black Death, Spanish Flu, HIV/AIDS, Swine Flu, Ebola virus, Zika virus, Corona viruses such as: SARS-Cov, MERS-Cov, COVID-19
Summary
Population ecologists use methods to model the population dynamics. An accurate model should be able to describe the changes occurring in a population and predict future changes. Anybody knows the importance and effect of single species in community and nature, and so we present a summary and brief literature of mathematical models such as single species, exponential and logistic modeling used to describe population dynamics, which may help us future model development and highlights the importance of population growth rate modeling in biology, ecology, and another area even computer and network sciences. Anybody is able to find out the answer of question ”How great an effect does self-generated spatial structure have on logistic population growth?” which is studied by Law et al in [7] They showed that population growth given by logistic model may differ greatly from that of the nonspatial logistic equation. Some of them are microbiology (growth of bacteria), conservation biology (restoration of disturbed populations), insect rearing (prediction of yield), plant or insect quarantine (population growth of introduced species), fishery (prediction of fish dynamics), biochemical(radioactivity)
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