On the number of limit cycles in small perturbations of a piecewise linear Hamiltonian system with a heteroclinic loop (Q266197)
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scientific article; zbMATH DE number 6567959
| Language | Label | Description | Also known as |
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| English | On the number of limit cycles in small perturbations of a piecewise linear Hamiltonian system with a heteroclinic loop |
scientific article; zbMATH DE number 6567959 |
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On the number of limit cycles in small perturbations of a piecewise linear Hamiltonian system with a heteroclinic loop (English)
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13 April 2016
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The authors consider limit cycle bifurcations for a class of non-smooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic loop around the origin. When the degree of perturbing polynomial terms is \(n,\) it is obtained that \(n\) limit cycles can appear near the origin and the heteroclinic loop respectively by using the first Melnikov function of piecewise near-Hamiltonian systems. Especially, for \(n=1,2,3,4,\) a precise result on the maximal number of zeros of the first Melnikov function is derived.
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piecewise smooth system
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bifurcation
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limit cycle
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heteroclinic loop
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Melnikov function
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Chebyshev system
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