Bifurcation from chaos to periodic states in bidirectional interconnected Lorenz systems by the variation of the coupling strengths

Abstract

Abstract After analyzing the resulting states of two bidirectionally linear interconnected Lorenz systems by the variation of the coupling strengths a bifurcation from chaos to period have been detected. The systems lose asymptotical stability as the coupling strengths takes specific values. These coupling strengths have been adjusted in order to be opposite in sign (i.e., one positive and one negative), and can be considered as a bifurcation parameter on the states of the resulting trajectories. The coupled system has been studied by means of bifurcation analysis, the distance between the resulting trajectories and the standard deviation along the iterated time. Numerical examples of the phase states of the coupled systems along with the bifurcation graphs are presented in order to visualize the resulting chaotic or periodic trajectories as well as the synchronized states.