Existence criteria for cycles in two-dimensional quadratic systems (Q946002)

The author has shown in previous papers that planar quadratic systems can be transformed to a special Liénard-type system with discontinuous nonlinear functions. In this way, a new asymptotic method can be developed to study conditions for the existence of limit cycles in quadratic systems. Some of them are demonstrated in this paper. Especially, the author shows that two Hopf bifurcations can occur in quadratic systems at different equilibria at the same time when a control parameter passes a critical value.