Abstract
The Biomathematics or Mathematics Biology is the study of biological phenomena using mathematical tools of varying complexity. For modeling and analyzing are ordinary differential equations, partial differential equations and / or stochastic differential equations. In this area, interested in investigating the evolution of species and the relationship with their environment (predation, competition, presence and quality of food, symbiosis and mutualism, etc.), To predict the future evolution of the ecosystems under certain conditions, introduce techniques to control them. In this article, we focus on the present version of a variant the model deterministic and stochastic LotkaVolterra predator-prey, two populations, consisting of the simultaneous differential equations system, where x and y represent the number of prey and predators, respectively, with A, B, C, D positive constants, which reflect the growing conditions of species and their interactions. The study of these issues appears to be of great importance in areas such as renewable resource management, development of varieties resistant to pesticides, technology substitution phenomena, organizational change or organizational learning.
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