A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic equation associated with the model, a bifurcation diagram was drawn in an appropr...A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory.展开更多
In this paper, we study a simplified model with delay for a control oftestosterone secretion. Employing the ejective fixed point principle due to Nussbaum, the existenceof slowly oscillating periodic solution of the m...In this paper, we study a simplified model with delay for a control oftestosterone secretion. Employing the ejective fixed point principle due to Nussbaum, the existenceof slowly oscillating periodic solution of the model is proven when the delay parameter r 】 r_0, forsome constant r_0 】 0.展开更多
文摘A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory.
基金Supported by the National Natural Science Foundation of China (No.19831030)The thesis is the production of the natural science research item for the 10th five-year plan in Jilin province office of education (No.200433).
文摘In this paper, we study a simplified model with delay for a control oftestosterone secretion. Employing the ejective fixed point principle due to Nussbaum, the existenceof slowly oscillating periodic solution of the model is proven when the delay parameter r 】 r_0, forsome constant r_0 】 0.
