Stability and Hopf bifurcation analysis in bidirectional ring network model

Using the system parameter instead of the delay as the bifurcation parameter, linear stability and Hopf bifurcation analysis including its direction and stability of bidirectional ring network model are investigated in this paper. The main tools to obtain our results are the normal form method and center manifold theory. Numerical simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior.

Research highlights► Exploit the system parameter instead of the delay as the bifurcation parameter. ► Study linear stability and Hopf bifurcation analysis including its direction and stability. ► The main tools to obtain our results are the normal form method and center manifold theory.