Maximum number of periodic solutions of certain differential equations
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Date
2024
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University 20 Aout 1955-Skikda
Abstract
This 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 results
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Keywords
periodic solutions/differential equations