Criterion to identify Hopf bifurcations in maps of arbitrary dimension.
The classical Hopf bifurcation criterion is stated in terms of the properties of eigenvalues. In this paper, a criterion without using eigenvalues is proposed for maps of arbitrary dimension. The parameter mechanism of Hopf bifurcation may be explicitly formulated on the basis of the criterion. A numerical example demonstrates that the proposed criterion is preferable to the classical Hopf bifurcation criterion in theoretical analysis and practical applications.
Wen
Guilin
G
Key Laboratory of Advanced Technology for Vehicle Body Design & Manufactory, MOE, College of Mechanical and Automotive Engineering, Hunan University, Changsha, Hunan 410082, People's Republic of China. wenguilin@yahoo.com.cn