Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization

Abstract EN

Two ellipsoidal ultimate boundary regions of a special three-dimensional (3D) chaotic system are proposed.

To this chaotic system, the linear coefficient of the i th state variable in the i th state equation has the same sign; it also has two one-order terms and one quadratic cross-product term in each equation.

A numerical solution and an analytical expression of the ultimate bounds are received.

To get the analytical expression of the ultimate boundary region, a new result of one maximum optimization question is proved.

The corresponding ultimate boundary regions are demonstrated through numerical simulations.

Utilizing the bounds obtained, a linear controller is proposed to achieve the complete chaos synchronization.

Numerical simulation exhibits the feasibility of the designed scheme.