Most of real life problems involve nonlinear systems (predator-prey model is one such example). The nonlinear system are very hard to solve explicitly but qualitative and numerical techniques may help shade some information on the behavior of the solutions. It should be noted also that we succeeded in developing an explicit technique for linear system. So somehow we are able to sat something about the linear ones. So the question is how do we relate the two kinds, that is the linear and nonlinear systems. The main idea is to approximate a nonlinear system by a linear one hoping that the conclusions on one will be the same as the other one. This is called linearization of nonlinear systems.
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Author: Mohamed Amine Khamsi