Controlabilidade local para um modelo Lotka-Volterra

In this article, we apply the tools of mathematical controllability theory in biological models. The approximation method around equilibrium solutions was used to study the local controllability of Lotka-Volterra systems, which model population dynamics between prey and predator species. We performed an analysis to determine if specific problems of the Lotka-Volterra type have the property of local controllability, which is guaranteed for certain equilibrium points. This property consists of guaranteeing the existence of a control, u in L^infinite([0,tau];R), such that the solution satisfies x_1(tau)=x_{1,1} and x_2(tau)=x_{2,1} for each pair {(x_{1,0},x_{2,0}) ,(x_{1,1},x_{2,1})} in a neighborhood of some equilibrium point of the system, where x_1(t), x_2(t) denote the populations of prey and predator species, respectively, at time t>0 e x_{1,0}, x_{2,0} are the initial populations.