Hopf Bifurcation Analysis of Nonlinear Rössler Systems

Abstract

The Hopf bifurcation problem of nonlinear Rössler system with time delay is studied. The Hopf bifurcation conditions of the Rössler system with nonlinear delay are given, the Hopf bifurcation points of the system delay parameters are obtained, and the stability of the system near the delay bifurcation points is analyzed. The simulation results show that the supercritical Hopf bifurcation occurs in the time-delay bifurcation point of the nonlinear Rössler system, and the changes of the time-delay parameters near the time-delay bifurcation point will affect the stability of the system.