Non-linear bifurcation analysis of non-gradient systems

The post-divergence behaviour of non-gradient systems is studied through a perturbation approach, attention being restricted to equilibrium paths in the neighbourhood of a critical point. Simple and coincident critical points are treated separately. Various characteristic phenomena are explored in general terms by identifying certain distinct properties of the Jacobian matrix in a state-space formulation. It is demonstrated that the well-known asymmetric and symmetric points of bifurcation can also arise in non-gradient systems and the conditions giving rise to each of these phenomena are discussed. An illustrative example is presented.