ABSTRACT

Chaos Control Delay feedback control (DFC) method was brought forward by K. Pyragas [14]. The method allows a noninvasive stabilization of unstable periodic orbits (UPOs) of dynamical systems [15]. It feeds back part of system output signals as exterior input to the system after a time delay. ( )u • is control signal gained by self-feedback coupling between output and input signals in chaotic system. ( ) ( )( ) ( )tutxftx +−= 1 is the form of DFC, where

τα (5.1)

From Fig. 3.1 we know that chaos exists in system (3.1) when 3.2,4.0 12 == αα , therefore we carry out control under this condition .Choosing 1=τ , fi rst inspect the relation of k and system stability. The Jacobian matrix of system (5.1) is:

(5.2)

Substitute equilibrium point (0.4,0.9) into (5.2), we obtain eigenvalues

1 2 1.70.83,

1 k

k λ λ −= − =

+ . So when 35.0>k , absolute values of both eigenvalues are less

than 1, which means the system is stable.