Journal of Mahani Mathematical Research
Volume:4 Issue: 2, Summer and Autumn 2015

‎In this paper‎, ‎a coherent system consisting of non-identical dependent active components and‎ ‎equipped with non-identical dependent standby components is considered‎. ‎The main object of this study is the random quantity‎ ‎which account the number of surviving standby components when the system‎ ‎is failed‎. ‎We represent the distribution function of the corresponding random variable in terms of‎ ‎system signature‎.

In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration model as operator Equation, apply orthogonal decomposition, compute the center manifold and normal form we determined the direction and stability of bifurcating periodic solutions. Therefore the Hopf bifurcation of the model became controllable to achieve desirable behaviour which are applicable in certain circumstances.