Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
2645-4505
4
2
2015
08
01
The behavior of non-identical and dependent standby components in a coherent system
39
50
EN
Heshmatolah
Jamali
Department of Mathematics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
hm.jamali@yahoo.com
Mohsen
Rezapour
Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
mohsenrzp@gmail.com
10.22103/jmmrc.2017.1657
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.
Stochastic ordering,Archimedean copula,order statistics,standby redundancy,reliability systems
http://jmmrc.uk.ac.ir/article_1657.html
http://jmmrc.uk.ac.ir/article_1657_d11a83aca040f1cc4f35dac2fc3418bd.pdf
Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
2645-4505
4
2
2015
08
01
HOPF BIFURCATION CONTROL WITH PD CONTROLLER
51
57
EN
M.
Darvishi
DEPARTMENT OF MATHEMATICS, FACULTY OF MATHEMATICS AND STATISTICS, UNIVERSITY OF BIRJAND, BIRJAND, IRAN
m.darvishi@birjand.ac.ir
H.M.
MOHAMMADINEJAD
DEPARTMENT OF MATHEMATICS, FACULTY OF MATHEMATICS AND
STATISTICS, UNIVERSITY OF BIRJAND, BIRJAND, IRAN
hmohammadin@birjand.ac.ir
10.22103/jmmrc.2017.1658
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.
Hopf bifurcation,Bifurcation control,PD Controller,Stability,Time delay
http://jmmrc.uk.ac.ir/article_1658.html
http://jmmrc.uk.ac.ir/article_1658_d67a40179b767cbf5395dcddb6c594e0.pdf