期刊
NONLINEAR DYNAMICS
卷 50, 期 3, 页码 575-585出版社
SPRINGER
DOI: 10.1007/s11071-006-9175-0
关键词
border-collision bifurcations; continuation methods; grazing; hybrid dynamical systems; limit cycles; piecewise smooth dynamics; shooting methods
Physical limits place bounds on the divergent behaviour of dynamical systems. The paper explores this situation, providing an example where generator field-voltage limits capture behaviour, giving rise to a stable, though non-smooth, limit cycle. It is shown that shooting methods can be adapted to solve for such non-smooth switching-induced limit cycles. By continuing branches of switching-induced and smooth limit cycles, the paper established the co-existence of equilibria, smooth and non-smooth limit cycles. Furthermore, it is shown that when branches of switching-induced and smooth limit cycles merge, the limit cycles are annihilated at a grazing bifurcation.
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