Applying Dynamic Systems to Social Media by Using Controlling Stability
Àbdulsattar Abdullah Hamad, M. Lellis Thivagar, Malik Bader Alazzam, Fawaz Alassery, Fahima Hajjej, Ali A. Shihab
Abstract
This study focuses on hybrid synchronization, a new synchronization phenomenon in which one element of the system is synced with another part of the system that is not allowing full synchronization and nonsynchronization to coexist in the system. When <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:munder><a:mrow><a:mi mathvariant="normal">lim</a:mi></a:mrow><a:mrow><a:mi>t</a:mi><a:mo>⟶</a:mo><a:mi>∞</a:mi></a:mrow></a:munder><a:mi>Y</a:mi><a:mo>−</a:mo><a:mi>α</a:mi><a:mi>X</a:mi><a:mo>=</a:mo><a:mn>0</a:mn></a:math> , where Y and X are the state vectors of the drive and response systems, respectively, and Wan ( <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" id="M2"><d:mi>α</d:mi></d:math> = <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" id="M3"><f:mo>∓</f:mo></f:math> 1)), the two systems’ hybrid synchronization phenomena are realized mathematically. Nonlinear control is used to create four alternative error stabilization controllers that are based on two basic tools: Lyapunov stability theory and the linearization approach.