The purpose of this study is to explore a class of general differential-difference equations with recurrent neural feedback. First, we investigate the local stability of the zero solution of the equations by analyzing the corresponding characteristic equation of the linearized equation. General stability criteria involving the delays and the parameters are obtained. Second, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits the Hopf bifurcation. The stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory. Finally, we applied to a special model.
|Effective start/end date||2018/08/01 → 2019/10/31|
- general differential-difference equations with recurrent neural feedback; Hopf bifurcation
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