الفهرس 
Chapter 1: IntroductionOnly 14 pages are availabe for public view
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Abstract
This thesis is concerned with the study of Parkinson’s disease, which considered one of the most widespread neurological diseases after Alzheimer’s disease and appears as a result of a defect in the neurons responsible for producing dopamine, which affects the motor system. This study included some mathematical studies of Parkinson’s disease, in particular the mathematical models that use delay differential equations. Some mathematical models are presented using graph theory and circle map. This thesis consists of five chapters: Chapter I : In this chapter, the medical aspect of the disease was presented, the symptoms of the disease and its environmental, genetic reasons, and the physiology of Parkinson’s disease are presented, and also the methods of treatment with drugs, surgery, and deep brain stimulation are presented. Chapter II : In this chapter, we are developed the Parkinson’s disease models using differential equations. The use of the Van der Pol model in the study of the disease, the importance of graph theory in relation to modeling Parkinson’s disease mathematically, and the importance of the circle map in modeling the disease mathematically are discussed. Chapter III : In this chapter, a model of Parkinson’s disease was presented using the delay differential equations, and the stability conditions are studied for each model. The modification was made to this model to make it more consistent with the biological model and more generalized. Some numerical examples are simulated to improve our discussion of the models. Chapter IV : In this chapter, the step method is used for solving delay differential equations and comparing the solution with the Matlab code dde 23 in solving delay differential equations. An analytical solution of the delay differential equations is approximated. Chapter V : In this chapter, the models are presented in the previous two chapters are studied, and the conditions for the Hopf bifurcation are investigated for these models. Numerical simulation of these models is studied using the Matlab program. At the end, we have the References and Appendix sections.