Analytical Hopf Bifurcation and Stability Analysis of T System

Complex dynamics are studied in the T system,a three-dimensional autonomous nonlinear system.Inparticular,we perform an extended Hopf bifurcation analysis of the system.The periodic orbit immediately followingthe Hopf bifurcation is constructed analytically for the T system using the method of multiple scales,and the stabilityof such orbits is analyzed.Such analytical results complement the numerical results present in the literature.Theanalytical results in the post-bifurcation regime are verified and extended via numerical simulations,as well as by theuse of standard power spectra,autocorrelation functions,and fractal dimensions diagnostics.We find that the T systemexhibits interesting behaviors in many parameter regimes.