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Limit cycle bifurcations of near-Hamiltonian systems with multiple switching curves and applications

  • * Corresponding author: Maoan Han

    * Corresponding author: Maoan Han

Celebrating the 80th Birthday of Professor Jibin Li

Supported by National Natural Science Foundation of China (No.11931016)

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  • In the present paper, we are devoted to the study of limit cycle bifurcations in piecewise smooth near-Hamiltonian systems with multiple switching curves, obtaining a formula of the first order Melnikov function in general case. As an application, we give lower bounds of the number of limit cycles for a piecewise smooth near-Hamiltonian system with a closed switching curve passing through the origin under piecewise polynomial perturbations.

    Mathematics Subject Classification: Primary: 37G15, 34A36; Secondary: 34C23.


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  • Figure 1.  The orbit $ \widehat{AB_{\varepsilon}A_{\varepsilon}} $ of system (3)

    Figure 2.  The orbit $ \widehat{A_{1}A_{2\varepsilon}A_{3\varepsilon}A_{1\varepsilon}} $ of system (18) for $ m = 3 $

    Figure 3.  Periodic orbits and switching curve of system (23)$ |_{\varepsilon = 0} $

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