Small limit cycles bifurcating from z_4-equivariant near-hamiltonian system of degrees 9 and 7

摘要

In this paper, we study the number and distribution of small limit cycles of some Z_4-equivariant near-Hamiltonian system of degree 9. Using the methods of Hopf bifurcation theory, we find that this system can have 64 small limit cycles. The configuration of 64 small limit cycles of the system is also illustrated in Fig. 1. When we let some parameters be zero, then we find that there can be 40 small limit cycles in a seventh system.