Effect of optimal uncoupling in enhancing synchronization stability in drive-response systems

Abstract

In this paper, we report the implementation of the method of optimal uncoupling and its effect in enhancing the stability of synchronization in certain coupled third-order chaotic systems. The clipping of phase space of the response system to a finite width having certain orientation about the coordinate axes representing the state variables of the response system insists that those state variables are coupled with their counterpart of the drive system. The stability of synchronization is studied through the master stability function (MSF). The optimal directions of implementing the clipping width to achieve stable synchronization is observed by studying the effectiveness of the 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 the 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 the implication of the clipping width is discussed and the range of orientation over which the clipping width has to be varied is generalized.