Lorenz and Lotka-Volterra Equations Using MATLAB Resolution

Abstract

In Mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.Mainly the study of differential equations consists of the study of their solutions, and of the properties of their solutions.Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.In our report, we are interested by the resolution of two differential equations, the famous Lorenz dynamic system which was developped to understand the chaotic character of meteorology, and the Predator prey model.In the folowwing report, we are going to resolve these equations in order to understand their meanings using Matlab, but first of all, we should introduce each problem, then develop and explain both mathematical and numerical issues, our main goal is to resolve these systems with an adequate Matlab formulation, using the ode45 function and finally we should discuss the results.