Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
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DOI：
10.1088/0951-7715/12/4/321
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发表时间：
1999-07
期刊：
影响因子：
1.7
通讯作者：
C. Christopher;S. Lynch
中科院分区：
文献类型：
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作者：
C. Christopher;S. Lynch
我们考虑二阶方程，其中f和g是多项式，且deg f，deg g n。我们感兴趣的是孤立的周期解，可以从稳定状态解x = 0分叉的最大数量。或者，这相当于寻求极限环的最大数量，可以分叉的起源李？nard系统，假设原点不是中心，我们证明了，如果f或g是二次的，那么这个数是。如果f或g是三次的，我们证明这个数是，对所有1n50。结果也适用于广义李？Nard系统
We consider the second-order equation where f and g are polynomials with deg f,deg g n. Our interest is in the maximum number of isolated periodic solutions which can bifurcate from the steady state solution x = 0. Alternatively, this is equivalent to seeking the maximum number of limit cycles which can bifurcate from the origin for the Li?nard system, Assuming the origin is not a centre, we show that if either f or g are quadratic, then this number is . If f or g are cubic we show that this number is , for all 1n50. The results also hold for generalized Li?nard systems.