| Citation: |
Jihua Yang. LIMIT CYCLE BIFURCATIONS IN A CLASS OF PIECEWISE SMOOTH DIFFERENTIAL SYSTEMS UNDER NON-SMOOTH PERTURBATIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2245-2257. doi: 10.11948/20200346
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LIMIT CYCLE BIFURCATIONS IN A CLASS OF PIECEWISE SMOOTH DIFFERENTIAL SYSTEMS UNDER NON-SMOOTH PERTURBATIONS
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Abstract
This paper deals with the problem of limit cycles of a class of piecewise smooth integrable differential systems with switching line $ x = 0 $. The generating functions of the associated first order Melnikov function satisfy two different Picard-Fuchs equations. By using the property of Chebyshev space, we obtain an upper bound for the number of limit cycles bifurcating from the period annulus under non-smooth perturbations of polynomials of degree $ n $. Finally, we present a concrete example to illustrate the theoretical result.
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References
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Jihua Yang. LIMIT CYCLE BIFURCATIONS IN A CLASS OF PIECEWISE SMOOTH DIFFERENTIAL SYSTEMS UNDER NON-SMOOTH PERTURBATIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2245-2257. doi: 10.11948/20200346
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Figure 1. The closed orbits of system (1.1)
$ |_{\varepsilon = 0}. $ -
Figure 2. The closed orbits of system (3.1)
$ |_{\varepsilon = 0}. $