Multiple delay Rössler system—Bifurcation and chaos control

Abstract

Multiple delayed Rössler system is analyzed from the view point of stability and chaos control. Usually these systems occur in active sensing problems where a signal is transmitted and received at a later time. Analytical and numerical results are obtained from the basic characteristic equation, using the Routh–Hurwitz criterion and Sturm sequences. The bifurcation pattern as the delay increases is displayed in detail, finally leading to chaos. In the second half we analyze the structure of the unstable periodic orbits and construct the controller which gets back the system to periodic state. Quantitative measure of the accuracy of the computation is obtained through the use of conditional Lyapunov exponent. At this point a Galerkin projection technique is used, which sets up a system of ODE in place of the delayed system, and makes the computation much simpler. Importance of this analysis is due to the role of the delay terms in the generation of the attractor, various bifurcation scenario, along with their control.