Journ´ ees d’Analyse Num´ erique et d’Optimisation Essaouira-Maroc 30 Octobre au 1 Novembre 2013 High gain observer for Lotka Volterra system Souad Najoua Lagmiri a , El Houssine El Mazoudi b , Noureddine Elalami c 1 a,c Laboratoire d’Automatique et Informatique Industrielle Ecole Mohammadia d’Ing´ enieurs Avenue Ibn Sina 765, Agdal Rabat, Maroc najoua.lagmiri@gmail.com. elalami@emi.ac.ma. b Laboratoire de Recherche en Economie de l’Energie, Environnement et Ressources, D´ epartement d’Economie University Caddy Ayyad, Marrakech, Maroc h mazoudi@yahoo.f r. Abstract. In the present paper, we construct a nonlinear observer for the continuous model of the Lotka-Volterra equations. A theoretical frame is provided in order to show the convergence charac- teristics of the proposed observer under some satisfied assumptions. The proposed methodology is applied to a class of Lotka−Volterra systems with two species. Numerical simulations are shown to validate and demonstrate the effectiveness of the proposed high gain observer. Key words: Lotka-Volterra System, Observer, Population Dynamics. AMS subject classification: Probability theory and stochastic processes, Biology and other natu- ral sciences , Systems theory, Control. 1. Introduction Let consider system defined by:  ˙ x 1 = x 1 (α − βx 2 ) ˙ x 2 = x 2 (−γ + δx 1 ) (1) y = x 1 (2) 1 Orator : S.N.LAGMIRI. Email: najoua.lagmiri@gmail.com 1