The divergence criterion has been shown to be helpful in distinguishing between suband supercritical Hopf bifurcations but its applicability is limited to systems whose divergence is sign definite. A step by step computational procedure which allows one to extend the applicability of the divergence criterion is derived by altering the system to an equivalent one with sign definite divergence. T...

Analysis of saddle-node and Hopf bifurcations in IFOC drives due to errors in the estimate of the rotor time constant is presented. Experimental results showing such bifurcations are given and guidelines for drive commissioning are derived from these results.

A formal framework for the analysis of Hopf bifurcations in delay differential equations with a single time delay is presented. Closed-form linear algebraic equations are determined and the criticality of bifurcations is calculated by normal forms.

Macroscopic systems with dissipation and time-modulated injection of energy, parametrically driven systems, can self-organize into localized states and/or patterns. We investigate a pulse that travels over a one-dimensional pattern in parametrically driven systems. Based on a minimal prototype model, we show that the pulses emerge through a subcritical Andronov-Hopf bifurcation of the underlyin...

In this paper, we study the dynamics and stability of a fundamental power system model when a time delay is imposed on the excitation of the generator. It is observed that sustained oscillations can arise in an otherwise stable power system through a delay induced Andronov-Hopf bifurcation. Numerical simulations are conducted to explore the dynamics of the time delayed system after the bifurcat...

We consider parameter-dependent, continuous-time dynamical systems under discretizations. It is shown that Hopf-Hopf bifurcations are O(h)-shifted and turned into double Neimark-Sacker points by general one-step methods of order p. Then we discuss the effect of discretization methods on the emanating Hopf curves. The numerical approximation of the critical eigenvalues is analyzed too. The resul...