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The primary objectives of the investigation are to analyze the dynamical behavior of an inertial shaker near the 1:4 strong resonance point by theoretical analyses and numerical simulation. Based on deriving the Poincaré mapping of the inertial shaker, a center manifold theorem technique is applied to reduce the Poincaré mapping to a two-dimensional one, and the normal form mapping associated with...
The dynamical characteristics of a single neuron model with time delay under periodic stimuli are studied in this paper. The analysis of the linear stability and the existence of Hopf bifurcation are given. Some numerical stimulations justify that the results of the analytical method are valid by a comparison with those of direct numerical integration.
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