Abstract
In this paper, a general two-neuron model with distributed delays, self-feedbacks and a weak kernel is studied. It is shown that the Hopf bifurcation occurs as the bifurcation parameter, the mean delay, passes a critical value where a family of periodic solutions emanate from the equilibrium. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of the bifurcation critical point of the mean delay is determined. The direction and the stability of bifurcating periodic solutions are determined by the Nyquist criterion and the graphical Hopf bifurcation theorem. Numerical simulation results supporting the theoretical analysis are also given.
Original language | English |
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Pages (from-to) | 206-213 |
Number of pages | 8 |
Journal | Neurocomputing |
Volume | 99 |
DOIs | |
Publication status | Published - 2013 |
Keywords
- Hopf bifurcation
- Nyquist criterion
- distributed delays
- frequency domain
- neural network
- neuron
- peiodic solutions
- stability