Properties Chaotic of Rabinovich-Fabrvikant Equations

درسنا معادله  رابينوفيتش ودرسنا الخواص العامه لها ووجدنا مناطق التقلص والتوسيع وكذلك وجدنا خواصها الفوضوية حيث برهنا أنها تحتوي على تبولوجي انتروبي موجبا وتمتلك حساسية عند الشروط الابتدائية وإنها متعديه باستخدام برنامج ماتلاب وبرهنا توسيع ليبانوف  الموجب وأخيرا درسنا بعد ليبانوف لهذه ألدالهWe give a new map named (Rabinovich-Fabrvikant equations) and  find five fixed points  we study only one fixed point  x0(0,0,0),  and  all general properties of them We prove  that the contracting and expanding  area of this point , thought the study of  the chaotic of  the point by use the Wiggins defined and we proof  that the lyapunov  exponent of the point  (0,0,0) is positive .We use matlab program to show sensitive dependence on the initial conditions and transitivity of (R-F)

Some Chaotic Properties of Ikeda Map

We study the dynamical system of Ikeda map on three dimension, we find some the general properties, and we show some chaotic properties of it. We prove the Lypaunov exponent of Ikeda map is positive and Ikeda map has sensitivity dependence to initial condition. Finally we use the Matlab program to draw the sensitivity of Ikeda map

Some Properties of Chaotic Modified of Bogdanov Map

In this  research to the modified dynamics of Bogdanov's map  studied, and the  found sensitivity to the initial conditions of the modified map  found as well as the Lyapunov exponent .the general characteristics of the map  by the diffeomorpism. Finally we boosted my research  with matlab to find chaotic area