Narrow Results

Most of the systems in an organism (human included) function in a regular daily rhythm. Hypothalamo-pituitary-adrenocortical (HPA) axis, although mostly known for its role in stress response, probably has a role in conveying rhythmic signals from the major pacemaker, suprachiazmatic nucleus (SCN), to the periphery. A general qualitative nonphenomenological mathematical model of the HPA axis is constructed and its dynamics is examined using linear stability analysis and Roushe's theorem. The results show that this system is asymptotically stable, i.e. it does not generate circadian oscillations, but only responds to the external pacemaker.

This paper takes the reaction–diffusion approach to deal with the quiescent females phase, so as to describe the dynamics of invasion of aedes aegypti mosquitoes, which are divided into three subpopulations: eggs, pupae and female. We mainly investigate whether the time of quiescence (delay) in the females phase can induce Hopf bifurcation. By means of analyzing the eigenvalue spectrum, we show that the persistent positive equilibrium is asymptotically stable in the absence of time delay, but loses its stability via Hopf bifurcation when time delay crosses some critical value. Using normal form and center manifold theory, we investigate the stability of the bifurcating branches of periodic solutions and the direction of the Hopf bifurcation. Numerical simulations are carried out to support our theoretical results.