Figure 1

Schematic representation of the three-scale wavelet decomposition of Fig. 2. The upper left square labeled by $L{L}_1$ corresponds to the lowest resolution subspace in both the horizontal and vertical directions. The information contained in this subspace is a coarse approximation of the original matrix. The other nine regions involve higher resolution subspaces, and they constitute the details of the original matrix at different scales. Among them, three diagonal regions labeled by $H{H}_3$, $H{H}_2$, $H{H}_1$ correspond to the highest resolution subspaces at each scale, and they contain the most detailed information of the original matrix in their scales.Reuse & Permissions

Figure 2

The impact of modifying a wavelet subspace to the coupling matrix $A$ of chaotic oscillators. (a) The original coupling matrix; (b) the three-scale wavelet decomposition of the original coupling matrix; (c) the modified wavelet decomposition (note the change in subspace $L{L}_1$); (d) the physical space image of the wavelet enhanced coupling matrix, $\tilde{A}$ obtained by the inverse wavelet transform of (c).Reuse & Permissions

Figure 3

Critical coupling strength ${\varepsilon }_c$ vs $K$ with the red line and green line denoting the effects of wavelet control in subspaces (1) $L{L}_1$ and (2) $H{H}_1$, $H{H}_2$, and $H{H}_3$, respectively. The horizontal green line indicates the nil impact of modifying high resolution subspaces to the transverse stability of synchronous manifold.Reuse & Permissions

Figure 4

Wavelet controlled dynamics showing the transition from chaos to periodicity. (a) The original chaotic states; (b) wavelet induced Hopf bifurcation from chaos.Reuse & Permissions