Limit Cycle Bifurcations from an Order-3 Nilpotent Center of Cubic Hamiltonian Systems Perturbed by Cubic Polynomials-Reference-Cited by-同舟云学术

Limit Cycle Bifurcations from an Order-3 Nilpotent Center of Cubic Hamiltonian Systems Perturbed by Cubic Polynomials

Published:2020-07 Issue:09 Volume:30 Page:2050126
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Zhang Li¹,Wang Chenchen²,Hu Zhaoping²^ORCID

Affiliation:

1. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, P. R. China

2. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China

Abstract

From [Han et al., 2009a] we know that the highest order of the nilpotent center of cubic Hamiltonian system is [Formula: see text]. In this paper, perturbing the Hamiltonian system which has a nilpotent center of order [Formula: see text] at the origin by cubic polynomials, we study the number of limit cycles of the corresponding cubic near-Hamiltonian systems near the origin. We prove that we can find seven and at most seven limit cycles near the origin by the first-order Melnikov function.

Funder

National Nature Science Foundation of China

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127420501266

Reference19 articles.

1. Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces

2. ON THE NUMBER OF LIMIT CYCLES IN NEAR-HAMILTONIAN POLYNOMIAL SYSTEMS

3. LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER

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