Robust Bifurcation Analysis Based on Degree of Stability

Consider nonlinear dynamical systems modelled by parameterised differential and difference equations. When the values of the system parameters vary from those at which the system is currently operated, it can exhibit qualitative changes in behaviour and a steady-state may disappear or become unstable through a bifurcation [1, 2]. Bifurcation analysis is clearly useful and a bifurcation diagram composed of bifurcation sets projected into parameter space displays various nonlinear phenomena in dynamical systems. On the other hand, when considering a steady-state which is closely approaching a bifurcation point due to unexpected factors like environmental changes, major incidents, and aging, self recovery is an important strategy for constructing a robust and resilient system. Traditional bifurcation analysis is not effective for this purpose because the global features of a bifurcation diagram in parameter