Saturday, November 23, 2013

Modeling Population Dynamics of Two Species with Volterra-Lotka Equations

Population kinetics is a study of biological and environmental process. It is very important in the real world which describes the changes in world size and age composition. Many of the most rouse dynamics in the biological world have to do with interaction between species. Mathematical sits which incorporate these interactions are consider to stimulate these dynamics. So, in the 1920s, the Italian mathematician Vito Volterra (1860-1940) and Alfred Lotka substantial the classical numerical model of a predator- feast situation. This model called the Voltera-Lotka predatory-prey model (Penny, 2004). The equations of Voltera-Lotka were developed in papers by Lotka in 1925 and Volterra in 1926. The fender administration discovered by both Volterra and Lotka independently consisted of cardinal entities. The model pull up stakes involve both equations if we consider only two species. One which describes how the prey populace changes and second which descr ibes how the predator population changes. One species, the predators feeds on the several(predicate) species, the prey which in figure out feeds on aforesaid(prenominal) food item readily uncommitted in the environment. A standard example is a population of foxes and rabbits in woodland. The foxes (predators) rust rabbits (prey), while the rabbits eat certain ve choosearian in the woodland.
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Other examples are sharks (predators) and food fish (prey), bass (predators) and sunfish (prey), ladybugs (predators) and aphids (prey), and beetles (predators) and scale insects (prey) (Penny, 2004). Beside the pre dator-prey situation, the opposite situatio! n that occurs in population dynamics is competing species. These situations involve two interacting populations which population and compete with severally other for the food in their same situation. Sometimes they will prey on ane another provided sometimes they will survive in peaceful. For example, two species of fish in a pond do not prey on each other but do compete for the available food. (C.DiPrima, 2010) In this...If you want to get a full essay, order it on our website: OrderCustomPaper.com

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