Some Mathematical Methods For The Study Of Biology Problems

This thesis concerns on some mathematical methods for solving biological problems.Firstly, we analyze the positive feedback and negative feedback in biology system. We focus on five kinds of biology systems:the autoactivating positive feedback system,the positive feedback system with two components, the positive feedback system with three components, mutual inhibition system and coupled positive and negative feedbacks. The system with positive feedback is easier to derive multistability, whereas the system with negative feedback is easier to be oscillating. For the system with only positive feedback, we find there is a kind of relationship between the bistability and the effect of the stimulus. For the mutual inhibition system, it just changes the bistable regime and the state quantity when we change the feedback. The interlinked positive and negative feedbacks can exhibit monostability, bistability and oscillation. However, if we change the sigmoidal function in the system, the system will show part of its characteristics.Dimensional theory is widely applied in the biology science and prompt inno-vative ways to promote a real progress in biology science, namely by understand-ing and analytically describing complex hierarchical scaling processes, chaotic disordered systems, non-linear dynamic phenomena, standard and anomalous transport diffusion events through membrane surfaces, morphological structures and biological shapes in physiological science. We study a useful way to calculate the dimension. We focus on the approximation problem of theβ-expansion over formal Laurent series field. The sets of formal Laurent series approximated by all orders are considered and such Hausdorff dimensions are obtained.