Tham khảo tài liệu 'chaotic system part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 214 Chaotic Systems Fig. 5. Error dynamics of the coupled master-slave Chen system when controller is switched on Anti-synchronization of two identical coupled chaotic Lee systems The studied chaotic Lee system is described by the following differential equations Juhn et al. 2009 x 1 t -10 10 0 _X1 t x2 t 40 0 -x1 t x2 t 62 _x s t _ _4X1 t 0 _x3 t _ It exhibits a chaotic attractor starting at the initial value of the state vector x o 2 3 2 T Fig. 6. Fig. 6. Three-dimensional view of the Lee chaotic attractor 215 Coexistence of Synchronization and Anti-Synchronization for Chaotic Systems via Feedback Control Let us consider the master Lee system Sm given by 63 xm1 t -10 10 0 xm1 t xm2 t 40 0 -xm1 t xm2 t 63 X m3 t . _4xm1 t 0 _xm3 t _ driving a similar controlled slave Lee system Ss described by 64 x s1 t Xs2 t Xs3 t -10 10 0 xs1 t 0 40 0 -xs1 t xs2 t 1 u t 4xs1 t 0 _xs3 t _ l_0 J 64 u t is the scalar active control. For the following state error vector components defined relatively to anti-synchronization study eAS1 t xs1 t xm1 t eAS2 t xs2 t xm2 t 65 eAS3 t xs3 t xm3 t the error system can be defined by the following differential equations eAS1 t 10eAS1 t 10eAS2 t ẻAS2 t 40eAS1 t - xs1 t xs3 t xm1 t xm3 t u t 66 ẻAS3 t t 4 x21 t x21 t The problem of chaos anti-synchronization between two identical Lee chaotic dynamical systems is solved here by the design of a state feedback structure kị . Vi 1 2 3 and the choice of nonlinear functions fi . Vi 1 2 3 such that 3 u t -i kị . x t - fj . Vj 1 2 3 67 i 1 It comes the following closed-loop dynamical error system eAS1 t eAS2 t -10 40 - k1 . 10 -k2 . 0 1 -k3 . eAS1 t eAS2 t - f1 l . xS1 i xs3 i xm1 t xm3 t f2 . _eAS3 t . 0 0 _eAS3 t . 4 x21 t xm1 t f3 . 68 The nonlinear elements fi . and ki . have to be chosen to make the instantaneous characteristic matrix of the closed-loop system in the arrow form and the closed-loop error system asymptotically stable. 216 Chaotic Systems From the .
