Mathematical analysis of the wavelet method of chaos control

In this paper, we provide mathematical analysis for the controllability of chaos in wavelet subspaces. We prove that depending on the scale of the wavelet operation and the number of the coupled oscillators, the critical coupling strength for the occurrence of chaos synchronization becomes many times smaller if the original coupling matrix is appropriately treated with the wavelet transform. Moreover, we obtain rigorous relations connecting the critical values and the wavelet subspace operations. Our mathematical results are completely consistent with early numerical simulations.