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

Jingnan Wang | Zendy; Weihua Jiang | Zendy

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

Author(s) -

Jingnan Wang,

Weihua Jiang

Publication year - 2013

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2013007

Subject(s) - control theory (sociology) , power (physics) , mathematics , singularity , computer science , mathematical analysis , physics , thermodynamics , artificial intelligence , control (management)

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.

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