Local controllability for a Lotka-Volterra model - Puma, Francis Félix Córdova (2024)
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.