A piece-wise linear planar neuron model, namely, two-dimensional McKean model with periodic drive is investigated in this paper. Periodical bursting phenomenon can be observed in the numerical simulations. By assuming the formal solutions associated with different intervals of this non-autonomous system and introducing the generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the bursting solution induced by the slowly varying periodic drive is presented. It is shown that, the discontinuous Hopf bifurcation occurring at the non-smooth boundaries, i.e., the bifurcation taking place at the thresholds of the stimulation, leads the alternation between the rest state and spiking state. That is, different oscillation modes of this non-autonomous system convert periodically due to the non-smoothness of the vector field and the slow variation of the periodic drive as well.
The studying standard of life sciences and clinical medicine is determined by the development level of morphology detection of biological cells. Currently, there are two approaches for revealing the 3D structure of biological cells, namly, interferometric technique and diffractive technique. Both methods could offer the phase information of the cell. Due to the translucent characteristics of cells and the wave nature of light based on cell scale, interference effect coexists with the diffraction effect when light passes through the cells. In this paper, models based on the shape of the typical blood cells are built and simulation experiments of interference as well as diffraction phase imaging are carried out with the models. Furthermore, the similarities and differences between them are discussed, with respect to the intensity distribution and phase distribution. The result agrees well with the experiments. It is suggested to be useful to promote the research of phase recovery methods of the two kinds of imaging technology.
A set of optical models associated with blood cells are introduced in this paper. All of these models are made up of different parts possessing symmetries. The wrapped phase images as well as the unwrapped ones from two orthogonal directions related to some of these models are obtained by simulation technique. Because the phase mutation occurs on the boundary between nucleus and cytoplasm as well as on the boundary between cytoplasm and environment medium, the equation of inflexion curve is introduced to describe the size, morphology, and substructure of the nuclear cell based on the analysis of the phase features of the model. Furthermore, a mononuclear cell model is discussed as an example to verify this method. The simulation result shows that characterization with inflexion curve based on orthogonal phase images could describe the substructure of the cells availably, which may provide a new way to identify the typical biological cells quickly without scanning.
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