Applying Dynamic Systems to Social Media by Using Controlling Stability

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$\underset{t⟶\infty }{\lim }Y-\alpha X=0$, where Y and X are the state vectors of the drive and response systems, respectively, and Wan ($\alpha$ = $\mp$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.