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.