Abdallah , BrikAmel, Boulfoul2025-12-162025-12-162024http://dspace.univ-skikda.dz:4000/handle/123456789/5593This thesis investigates the dynamics of periodic solutions and bifurcations in nonlinear dynamical systems. We use averaging theory to study the maximum number of isolated periodic solutions (i.e. limit cycles) in a second-order differential system. Also, using the same theory we examine zero-Hopf bifurcation for finding periodic solutions in a modified hyperchaotic Chen system and a three-dimensional Kolmogorov system. Through these studies, we demonstrate the emergence of limit cycles and establish conditions for their existence. We provide numerical examples to illustrate our resultsenperiodic solutions/differential equationsThesis