Qualitative and numerical study

Abstract

The objective of this thesis is the qualitative study of some classes of nonlinear planar polynomial 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, 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.