الفهرس 
Fundamental ConceptsOnly 14 pages are availabe for public view
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Abstract
The aims of this thesis are proposing and deduction of some models of nonlinear autoregressive, adding randomized noise and studying some of its dynamic properties such as stability conditions and analysis of points of diffraction, and studying the effect of the part responsible for the randomized noise.
This thesis starts with an introduction and sequentially followed by four chapters then ended by a list of references used.
Chapter One: Fundamental Concepts
This chapter presents basic and fundamental definitions, theorems and concepts that used in the thesis.
Chapter Two: Forced Process Feedback Nonlinear Autoregressive (FPFNAR) Model
In this chapter, the dynamical behaviour of the forced process feedback nonlinear autoregressive (FPFNAR) model is considered for different levels of noise intensity. The existence and stability of the equilibria of the deterministic system are studied. Numerical simulations are employed to show the model’s complex dynamics by means of the largest Lyapunov exponents, bifurcations, fractal dimension, time series diagrams and phase portraits. The phenomenon of noise-induced intermittency near tangent bifurcation is discussed. The flip and the Neimark-Sacker bifurcations are discussed. The stochastic
sensitivity function is studied.
Chapter Three: Functional-Coefficients Nonlinear Autoregressive Models
In this chapter a new functional-coefficients nonlinear autoregressive (FCNAR) time series model is presented. The complex dynamics of the model’s skeleton is studied by means of the largest Lyapunov exponents, bifurcations, time series diagrams and phase portraits. Flip bifurcation is investigated using center manifold theorem and bifurcation theory. Stochastic sensitivity function technique is used to analyze the noisy attractors.
The interrelationship between parameter changes and marginal distribution of the states is discussed. The effects of noise intensity on its dynamics and the phenomenon of noise induced limit cycles are also discussed via simulation.
Chapter Four: The Logestic Smooth Transition Autoregressive (LSTAR) Models
This chapter studies the dynamic behavior of the logistic smooth transition autoregressive (LSTAR) model for two regimes with order = 3. The existence and local stability of fixed points of the system were analyzed for one control parameter. The direction and the stability of the Neimark-Sacker bifurcation for the free noise system has been studied.
The chaotic behavior of the system was discussed in notion of phase portraits, bifurcation diagram, time series portraits and Lyapunov exponents. A simulation was carried out to verify the theoretical study. Also the stochastic sensitivity function of the system was studied.
Chapter Five: Complex Valued Forced Functional Coefficient Nonlinear Autoregressive (FFCNAR) Model
This chapter introduces one case of the functional coefficients autoregressive time series models (FCAR). The dynamical behavior of the proposed system is studied. The existence and local stability of the equilibrium points of the system are analyzed. For one control parameter, the chaotic behaviour of the system is discussed by means of phase portraits, bifurcation diagram, time series portraits and Lyapunov exponents. The correlation structure is obtained. Numerical simulation is used to verify the theoretical
study.