BIFURCATION OF LIMIT CYCLES IN A FOURTH-ORDER NEAR-HAMILTONIAN SYSTEM-Reference-Cited by-同舟云学术

BIFURCATION OF LIMIT CYCLES IN A FOURTH-ORDER NEAR-HAMILTONIAN SYSTEM

Published:2007-11 Issue:11 Volume:17 Page:4117-4144
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

HAN MAOAN¹,SHANG DESHENG²,ZHENG WANG²,YU PEI³

Affiliation:

1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

2. School of Mathematics and Information Science, Shandong University of Technology, Zibo 255049, P. R. China

3. Department of Applied Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7, Canada

Abstract

This paper is concerned with bifurcation of limit cycles in a fourth-order near-Hamiltonian system with quartic perturbations. By bifurcation theory, proper perturbations are given to show that the system may have 20, 21 or 23 limit cycles with different distributions. This shows that H(4) ≥ 20, where H(n) is the Hilbert number for the second part of Hilbert's 16th problem. It is well known that H(2) ≥ 4, and it has been recently proved that H(3) ≥ 12. The number of limit cycles obtained in this paper greatly improves the best existing result, H(4) ≥ 15, for fourth-degree polynomial planar systems.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127407019895

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