Mathematics

Using the hippocampal cell channel model, the transmission features of hippocampal system are under the research. The process of memory is simulated by stochastic resonance. By synaptic model, the hippocampus model is constructed, which analyzes the summation of postsynaptic currents in the network. The strong capacity of spatiotemporal encoding in the network indicates the features of CA3 network during the information transmission process in the hippocampus. Analyzing the memory expression in CA1 under PP signal from entorhinal cortex or SC postsynaptic current respectively, results show that the reason is that single subthreshold signal cannot cause memory and stochastic resonance of them. The modeling result with time delay of the synaptic transmission is in accordance with the experimental phenomena of action potential in the hippocampus.

A mathematical model of tumor angiogenesis, regulated by vascular endothelial growth factor (VEGF) and angiopoietins (Ang-1, Ang-2), is presented. The Overture numerical simulation of this model is developed, and the result analysis shows the characteristics of the density changing of endothelial cells, vascular endothelial growth factor and angiopoietins in the extra-cellular matrix in tumor angiogenesis. There is a discussion of the simulation results of the model under four different situations, which shows the different roles of VEGF, Ang-1, Ang-2 and their relationship in tumor angiogenesis.

The motion of organization center of three-dimensional untwisted scroll waves in excitable media with single diffusion is studied by singular perturbation method in this paper. The relation of curvature and the linear law are derived for untwisted organization center. These results have explicit physical meaning and are in good agreement with experiments