Effect of optimal uncoupling in enhancing synchronization stability in coupled chaotic systems

In this paper, we report a novel approach for studying the effect of optimal uncoupling on the stability of synchronization in coupled chaotic systems. The clipping of phase space of the driven system having an orientation along the coordinate axes revealing the nature of coupling of the state variables of coupled systems is identified in certain coupled third-order chaotic systems. The stability of synchronization is studied through the {\emph{Master Stability Function}} (MSF). The optimal directions of implementing the clipping width to achieve stable synchronization is observed by studying the effectiveness of clipping fraction and the sufficient range of orientation to identify the optimal directions is reported. The functional work steps for identifying the optimal directions are presented and the synchronization of the response system with the drive within the clipped region of phase space for different orientations of clipping width are studied. The stability of synchronization for different orientations of clipping widths and the two-parameter bifurcation diagram indicating the negative valued MSF regions obtained for the optimal direction of clipping width are presented. The application of the method of optimal uncoupling in identifying the direction of implication of clipping width is discussed and the range of orientation over which the clipping width has to be varied is generalized.
Comment: 19 pages, 8 figures