Control of noisy heteroclinic cycles

We develop a control strategy for strongly nonlinear dynamical systems possessing heteroclinic cycles connecting saddle points and subject to small random perturbations. In the absence of control, attracting cycles lead to solutions which exhibit intermittent behavior consisting of quiescent periods interrupted by rapid “bursts”. We show that suitable feedback control can retain solutions near the saddle points and hence reduce the typical bursting rate. The model studied and the form of control are motivated by our interest in reducing turbulence production in the boundary layer.