Synchronization and anti-synchronization of a new hyperchaotic Lü system with uncertain parameters via the passive control technique

Abstract

In this paper, the synchronization and anti-synchronization problems of a newly reported hyperchaotic Lü system with uncertain parameters are investigated based on the passive control technique. By introducing three output variables, the passive controllers are designed to achieve synchronization and anti-synchronization between two new hyperchaotic Lü systems. Moreover, the corresponding update laws of the parameters are given. Simulation results are provided to show the effectiveness of the proposed controllers.

Synchronization and Electronic Circuit Application of Hidden Hyperchaos in a Four-Dimensional Self-Exciting Homopolar Disc Dynamo without Equilibria

“…Many effective methods exist to deal with synchronization of chaotic and 2 Complexity hyperchaotic systems. These include active control [12][13][14][15][16][17][18][19][20], passive control [21], sliding mode control [22][23][24][25][26][27][28][29][30][31], adaptive control [32], and backstepping design [33]. Of these, active control is an important simple method used in the synchronization of nonlinear systems.…”

Circuit Implementation and Antisynchronization of an Improved Lorenz Chaotic System

“…With its further study, some scholars expand the concept of synchronization. They proposed the concept of chaotic antisynchronization and realized the antisynchronization [15][16][17][18][19] of different chaotic systems with different methods. Works [15,16] implemented the antisynchronization of two identical chaotic systems with coupled and nondirectional coupling, respectively.…”

“…Work [17] realized the antisynchronization of a class of chaotic systems based on the state observer. In work [18], synchronization and antisynchronization were implemented for a new hyperchaotic Lü system with uncertain parameters via the passive control technique. Therefore, the study on the antisynchronization of chaotic systems is of great potential market value.…”

Hyperchaos and bifurcations in a driven Van der Pol–Duffing oscillator circuit

“…with the possibility of having two positive Lyapunov exponents along with one zero and one negative. Beginning with the pioneering work of Rössler [31], the study of hyperchaos has witnessed tremendous research interest in the last three decades, in the fields of nonlinear circuits [23,31,43,4], secure communications [1,34,21], nonlinear optics [16], control and synchronization [37,6,44], to mention a few. Due to its great potential in technological applications, the generation of hyperchaos from nonlinear systems has recently become one focal topic for research [23,37,22,33].…”