AN APPROACH TO THE STABILITY OF THE GAUSE-LOTKA-VOLTERRA COMPETITION ECOLOGICAL MODEL USING THE ROUTH-HURWITZ CRITERION

In the qualitative study of systems ordinary differential equations, we can analyze dynamics solutions by observing whether small variations or modifications in initial conditions produce changes future, this intuitive idea was formalized and studied Lyapunov reflects concept stability. For both linear nonlinear stability using criteria to obtain Hurwitz type polynomials. paper, a prey-predator model where three species compete considering Gause effect generated Gause-Lotka-Volterra system, an analytical technique Hurwitz-type polynomials called Routh-Hurwitz criterion. This criterion provides necessary and/or sufficient system studying location roots characteristic polynomial associated with system. article describes presents method model, based on allows establishing asymptotic analyzing eigenvalues matrix said The research results allow region that interaction between species.