BOGDANOV-TAKENS SINGULARITY IN THE COMPREHENSIVE NATIONAL POWER MODEL WITH TIME DELAYS

Jingnan Wang; Weihua Jiang

doi:10.11948/2013007

2013 Volume 3 Issue 1

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Jingnan Wang, Weihua Jiang. BOGDANOV-TAKENS SINGULARITY IN THE COMPREHENSIVE NATIONAL POWER MODEL WITH TIME DELAYS[J]. Journal of Applied Analysis & Computation, 2013, 3(1): 81-94. doi: 10.11948/2013007

Citation:

Jingnan Wang, Weihua Jiang. BOGDANOV-TAKENS SINGULARITY IN THE COMPREHENSIVE NATIONAL POWER MODEL WITH TIME DELAYS[J]. Journal of Applied Analysis & Computation, 2013, 3(1): 81-94. doi: 10.11948/2013007

BOGDANOV-TAKENS SINGULARITY IN THE COMPREHENSIVE NATIONAL POWER MODEL WITH TIME DELAYS

Jingnan Wang^1,2,
Weihua Jiang¹

1 Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China;
2 Department of Applied Mathematics, Harbin University of Science and Technology, Harbin, 150080, China

Fund Project:

Abstract

Abstract

In this paper, the comprehensive national power model with time delays is studied. The condition that there is only one trivial equilibrium in the model is given. Based on the analysis of the distribution of the eigenvalues at the trivial equilibrium, it is found that the trivial equilibrium is a Bogdanov-Takens singularity. Using the center manifold theory and the normal form method, the normal form with delay and ratio parameters of the model is obtained. Furthermore, the topological structures of the model near the bifurcation point with the variation of these two parameters are given. The associated development situations of the comprehensive national power for some topological structures are discussed. Finally, some numerical simulations are performed to support the analytic results.
- Comprehensive national power /
- time delays /
- normal form /
- BogdanovTakens singularity
MSC: 34K18;37G05;37G10;91D10

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