This paper is devoted to the study of the stability of limit cycles of a nonlinear delay differential equation with a distributed delay. The equation arises from a model of population dynamics describing the evolution of a pluripotent stem cells population. We study the local asymptotic stability of the unique nontrivial equilibrium of the delay equation and we show that its stability can be lost through a Hopf bifurcation. We then investigate the stability of the limit cycles yielded by the bifurcation using the normal form theory and the center manifold theorem. We illustrate our results with some numerics

Abstract.Specific activator and repressor transcription factors which bind to specific regulator DNA sequences, play an important role in gene activity control. Interactions between genes coding such transcription factors should explain the different stable or sometimes oscillatory gene activities characteristic for different tissues. Starting with the model P53-MDM2 described into [6] and the process described into [5] we developed a new model of this interaction. Choosing the delay as a bifurcation parameter we study the direction and stability of the bifurcating periodic solutions. Some numerical examples are finally given for justifying the theoretical results.

Abstract. In this paper we investigate the impact of delayed tax revenues on the fiscal policy out-comes. Choosing the delay as a bifurcation parameter we study the direction and the stability of the bifurcating periodic solutions. With respect to the delay we show when the system is stable. Some numerical examples are finally given for justifying the theoretical results.

This paper studies the autonomous uncertain and stochastic systems with multiple delays, which describe a financial system involving the interest rate, the investment demand and the price index. For the deterministic model associated to the uncertain financial system, we set the conditions for the existence of the delay parameter value for which the model displays a Hopf bifurcation. For the stochastic system, we identify the differential equations for the mean value as well as for the square mean value. The last part of the paper includes numerical simulations and conclusions.

This paper is concerned with the deterministic and the stochastic delayed Kaldor–Kalecki nonlinear business cycle models of the income. They will take into consideration the investment demand in the form suggested by Rodano. The existence of the Hopf bifurcation is studied and the direction and the local stability of the Hopf bifurcation is also taken into consideration. For the stochastic model, the dynamics of the mean values and the square mean values of the model’s variables are set. Numerical examples are given to illustrate our theoretical results.