Limit cycles: qualitative and numerical study

Abstract

The objective of this thesis is the qualitative study of some classes of nonlinear planar poly-nomial differential systems. Firstly,we have studied the integrability and the existence of a non-algebraic limit cycle of a class of differential systems of degree even, moreover ,we have determined their explicit expression.On the other hand,we have introduced another class of differential systems of degree 6k+1,(k∈ N∗),we have studied their integrability ,and then we have shown that it has a two non-algebraic limit cycles explicitly given.We have given some examples to illustrate the results obtained for each class. Finally,we gave a description of the operation of the P4 software, which is used to draw the phase portrait of the solutions of planar polynomial differential systems.