The close relation between voltage instability point and loading limit is well known, thus the calculation of loading provides some information about voltage stability. Unfortunately, power system load flows diverge at or near singular solutions. In this paper, a new method is proposed to overcome this convergence problem by using a transforming parameter. This method stems from the BIFURCATION theory. The emphasis is on the saddlenode BIFURCATION that sometimes occur in power systems. In addition, based on the proposed method, a computational algorithm is developed to determine voltage-parameter curves. To analyze voltage problems such as voltage collapse, this procedure is utilized to determine loading limit and calculate voltage stability indexes. The developed techniques have some advantages such as the use of classic power flow equations with no increase in their dimension and enlarging the convergence domain by local elimination of singularity.

In this paper, the dynamic behavior of an immunosuppressive infection model, specifically AIDS, is analyzed. We show through a simple mathematical model that a sigmoidal CTL response can lead to the occurrence of transcritical BIFURCATION. This condition usually occurs in immunodeficiency virus infections (such as AIDS infection) in which viruses attack immune cells CD4+T. Our results imply that the dynamic interactions between the CTL immune response and HIV infection are very complex and in the CTL response, dynamics can exist the stable regions and unstable regions. At the end of the paper, numerical simulations are presented to illustrate the main results.

The main purpose of this paper is to study dynamics of stochastic chemostat model. In this order, Taylor expansions, polar coordinate transformation and stochastic averaging method are our main tools. The stability and BIFURCATION of the stochastic chemostat model are considered. Some theorems provide sufficient conditions to investigate  stochastic stability, $D$-BIFURCATION and $P$-BIFURCATION of the  model. As a final point, to show the effects of the  noise intensity and illustrate our theoretical results, some numerical simulations are presented.