The stochastic and deterministic analysis of Zeeman model

SUMMARY Two and theree dimension Zeeman Model is studied in this project. Stability analysis will be studied in that type. İt is made analysis for the station of typical relaxed fiber length. Approximate analytic solutions for Zeeman models will be obtained. Firstly, stability analysis will be carried out by adding 'delay' term to the two dimension Zeeman model. After that in this study, Zeeman model with the behaviour of thesolution which was developed by Zeeman was dealed in case of being a random variable which has 'p' tension normal distrubition by adding random stochastic effects which is known as heartbeat model and it is calculated variance, standart deviation, confidence interval, expected value with calculating first four moments of x heartbeat muscle fiber, also it is formed graph simülation for heartbeat model by using numerical methods. It is made stability analysis of differantial Zeeman model from fractional level. Also, it is obtained solution curves for derivates from different levels. İt is obtained stochasticZeemanmodel by adding Wiener process terms to two and three dimension Zeeman model. Thisobtained stokastic model is being solved with Milstein and Euler-Maruyama methods. It is compared the solutions of stokastic, deterministic Zeeman model with random effect. It is used Random Diferantial Transformation Method (RDDM) for the solution ofRandom Zeeman Heartbeat Model. Parameters and initial conditions are taken as randomvariables which has respectively Beta and Normal distrubitions. Approximate expectedvalue and variance of the system is calculated by making approximate analytical solution ofRandom Zeeman Model. It is used Modified Differantial Random Method which contains theusage of Laplace-Pade Approach conversion to increase the accuracy and ratio ofconvergence of the solution of slash serial which is obtained from RDDM. The results obtained from the solution of Random model and random behaviours of components are shown by the help of tables and graps. The solution behaviours of random models whicincludes random effects with Beta and Normal distrubitions are compared. Key Words: Zeeman Heartbeat Model, Stability Analysis, Wiener process, Delay, Euler-Maruyama, Milstein, Expected Value, Variance, Laplace-Pade Approximate, Random Differantial Transformation Method, Normal Distribution, Beta Distribution