Lorenz attractor - arose from an ODE model of the atmosphere.
Ordinary differential equations (ODE) are sophisticated tools in order to model various systems in the real world. I studied some applications of Contraction Mapping Principle to nonlinear ordinary differential equations. Because of various constraints with nonlinear ODE, we often have to work with a simplified (from the nonlinear ODE) form which is a linear ODE. I proved that under certain assumptions a nonlinear system and a linear system are asymptotically equivalent in the sense that the difference between two corresponding solutions under a homeomorphism tends to zero as time tends to infinity.