الفهرس 
Introduction to dynamical systemsOnly 14 pages are availabe for public view
 |  | from | 109 |  |  |
| | | from | 109 | | |
Abstract
Dynamical systems represent the branch of mathematics that provides tools to understand the behavior of solutions in systems that changes with time. Bifurcation is one of the interesting subjects in the field of dynamical systems in which we study how the solution changes as the parameters of the model change. The goal of this work is to study the dynamics that occur in three systems of nonlinear differential equations and the bifurcation that occurs in each system with the change of parameters. The thesis consists of four chapters as follows. In chapter one an introduction to continuous dynamical systems is presented. The methods to study nonlinear dynamics are revised. Also, the main elements and laws of electrical circuit are summarized. In chapter two two different configurations of coupled nonlinear memristor-based oscillators are investigated. In particular, the dynamics that occur for the cases of ladder coupled circuits and ring coupled circuits are studied. For each scheme of circuit coupling, the mathematical models are derived in multi-parameter form to describe the possible cases of employing identical or different nonlinearities. The multiple scales method is applied to each case to obtain the normal forms. The dynamical behaviors are studied and the stability regions in parameters space for each type of dynamics are induced to show the bifurcations in system. Numerical simulations are presented to verify the analytical results. In chapter three the dynamics of a chaotic system in multi-parameter form are studied. The sufficient condition of the existence and uniqueness of the solution is derived. Analytical methods including the multiple scales method and Lyaponuv coefficients with phase portraits of numerical In chapter four the conclusions and suggestions for future work are presented.