The qualitative analysis of a dynamical system of differential equations arising from the study of multilayer scales on pure metals II

We provide a qualitative analysis of the -dimensional dynamical system:

where is an arbitrary positive integer. Under mild algebraic conditions on the constant matrix , we show that every solution , , extends to a solution on , such that , for . Moreover, the difference between any two solutions approaches as . We then use this result to give a complete qualitative analysis of a 3-dimensional dynamical system introduced by F. Gesmundo and F. Viani in modeling parabolic growth of three-oxide scales on pure metals.

     

The influence of interplay of external and internal noise on the detection of weak stimulus in a cell system

The influence of interplay of external and internal noise on the detection of weak stimulus in a cell system was studied by using a mesoscopic stochastic model. When the stimulus was too weak to fire calcium spikes for the cell, separately, we found that calcium spikes could be induced by the external noise or internal noise, and internal signal stochastic resonance (ISSR) or internal noise stochastic resonance (INSR) occurred, respectively, so that the cell system could detect the weak stimulus through intracellular calcium spikes with the help of external noise or internal noise. When considering both of the noises, we found that internal noise could suppress ISSR, while external noise could enhance INSR in a certain range of external noise intensity. Interestingly, when the INSR occurs, the optimal size matched well with the real cell size, this was of significant biological meaning.