ON THE STUDY OF BIFURCATIONS IN DELAY-DIFFERENTIAL EQUATIONS: A FREQUENCY-DOMAIN APPROACH

被引：8
|
作者：
Gentile, Franco S. [1 ]
Moiola, Jorge L. [1 ]
Paolini, Eduardo E. [1 ]
机构：
[1] Univ Nacl Sur, IIIE, Alfredo Desages UNS CONICET, Dept Ingn Elect & Comp, RA-8000 Bahia Blanca, Buenos Aires, Argentina
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2012年 / 22卷 / 06期
关键词：
Time-delay systems; frequency-domain approach; bifurcations; van der Pol oscillator; DER-POL OSCILLATOR; TIME-DELAY; HOPF-BIFURCATION; 2-NEURON SYSTEM; FEEDBACK; VAN; STABILITY; CHAOS;
D O I：
10.1142/S0218127412501374
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An improved version of a frequency-domain approach to study bifurcations in delay-differential equations is presented. The proposed methodology provides information about the frequency, amplitude, and stability of the orbit emerging from Hopf bifurcation. We apply this method to different schemes of the delayed van der Pol oscillator. The time-delay dependence can appear intrinsically because of the system dynamics or can be intentionally introduced in a feedback loop. Also, a discussion about system controllability and observability is given for a proper and rigorous application of the frequency domain technique. Collateral findings involving some types of static bifurcations are included for completeness.
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页数：15
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