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Rasoul Asheghi Hamid R.Z. Zangeneh 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2398-2409
In this paper, we study the distribution and simultaneous bifurcation of limit cycles bifurcated from the two periodic annuli of the holomorphic differential equation , after a small polynomial perturbation. We first show that, under small perturbations of the form , where is a polynomial of degree 2m−1 in which the power of z is odd and the power of is even, the only possible distribution of limit cycles is (u,u) for all values of u=0,1,2,…,m−3. Hence, the sharp upper bound for the number of limit cycles bifurcated from each two period annuli of is m−3, for m≥4. Then we consider a perturbation of the form , where is a polynomial of degree m in which the power of z is odd and obtain the upper bound m−5, for m≥6. Moreover, we show that the distribution (u,v) of limit cycles is possible for 0≤u≤m−5, 0≤v≤m−5 with u+v≤m−2 and m≥9. 相似文献
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In this paper we study the limit cycles of the Liénard differential system of the form , or its equivalent system , . We provide sufficient conditions in order that the system exhibits at least n or exactly n limit cycles. 相似文献
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