1. HOPF BIFURCATION OF A TWO-NEURON NETWORK WITH DIFFERENT DISCRETE TIME DELAYS.
- Author
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LI, SHAOWEN, LIAO, XIAOFENG, LI, CHUNGUANG, and WONG, KWOK-WO
- Subjects
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BIFURCATION theory , *NUMERICAL solutions to nonlinear differential equations , *CHAOS theory , *ALGORITHMS , *SPATIAL analysis (Statistics) , *DELAY differential equations - Abstract
In this paper, a two-neuron network with different time delays is investigated. By analyzing the associated characteristic equation, we obtain the conditions for delay-dependent and delay-independent asymptotic stability, respectively. Furthermore, we find that if the delay is used as a bifurcation parameter, Hopf bifurcation would occur. The direction and stability of the bifurcating periodic solutions are determined by using the Nyquist criterion and the graphical Hopf bifurcation theorem. Some examples are included to illustrate our results. [ABSTRACT FROM AUTHOR]
- Published
- 2005
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