Lotka–Volterramodel..docxVIP

Jiayu ChenMarch 20 2015Computational ModelingShort paper #2 Predator-prey models are very important tools to study biomasses in bio- and ecosystems. Such models can be used to study different forms of predator-prey interaction. A famous example of such models is the Lotka-Volterra Model, which are developed by Vito Volterra and Alfred Lotka in the early 20th century. Vito Volterra is a famous Italian mathematician and physicist. He was born into a poor family but he was talented in mathematics. After World War I, he started to focus his study on mathematical biology mainly by reiterating and developing the work of Pierre Francois Verhulst. Lotka-Volterra model is the most important outcome during this period of time. He joined the opposition to the Fascist regime of Benito Mussolini in 1922, and later refused to take a mandatory oath of loyalty. He had to resign his university post and membership of scientific academies. After this occurrence, he spent most of years aboard and did not return to Rome until just before his death. Alfred Lotka is an Americanchemist, mathematician, demographer and ecologist. He grew up in Lviv and later came to the United States, where he contributed several theoretical articles on chemical oscillationsduring the early decades of 20th century. After 1935, he quit academic science and spent most of his time working in an insurance company. He became thepresident of the Population Association of America. In 1926, Volterra proposed a model to explain the overserved increase in predator fish, which is the predator in his model, corresponding decrease in prey fish, which is the prey in his model, in the Adriatic Sea. In 1925, Lotka developed a model using the equations studied by Volterra to describe a hypothetical chemical reaction in which the chemical concentrations oscillate. In his model, prey is some chemical reactant A and predator is some chemical product B. The Lotka-Volterra model with linear per capita growth rates isx˙=(b?py)x fo