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 , where Y and X are the state vectors of the drive and response systems, respectively, and Wan (α = ∓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.
Highlights
Alazzam et al.’ study [1] is an example
The revolutionary hyperchaotic system is regulated to an unstable equilibrium position or limit cycle using only one scalar controller with two state variables
Ere are some inequalities that are not correct, and Q14 is negatively defined, so the control failed to achieve hybrid synchronization between the two systems, and to overcome this problem, we update the P-matrix with the same control as follows: 1111 5 1
Summary
Alazzam et al.’ study [1] is an example. Control and hybrid three-dimensional synchronization (HPS) procedures are for a unique hyperchaotic system. Using Lyapunov’s direct approach, the HPS between two new hyperchaotic systems is studied. Dynamical systems have received a lot of attention It is one of the first attempts in a Lu model, and a new hyperchaotic model with three unstable equilibrium points is disclosed. Ere is another study which introduces another chaotic and hyperchaotic complex nonlinear, and this type has a significant stake in its phase-space behavior [7,8,9]. It has been organized in the previous time, for example, a 3D auto system, which is not differ-isomorphic with the Lorenz attractor. In the arrangement of values for a parameter k, [10] has proposed another 3D attractor that shows chaotic behavior in distinct respects and not diffeomorphic with Lorenz [11,12,13,14,15,16,17,18]. e first chaotic nonlinear system has been suggested by Lorenz [19,20,21,22] in which is a generalization of the Lorenz system. e Lorenz system’s messy structure is utilized
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