Dr Gul is an Assistant Professor at COMSATS University Islamabad, Abbottabad Campus, Pakistan. He received a PhD in Mathematics from Free University Berlin, Germany. His research is in he area of cardiovascular modeling, uncertainty quantification and sensitivity analysis. He published 12 research articles in well reputed journals and international conferences. Additionally, he supervised 6 MS students in COMSATS University Islamabad, Abbottabad Campus, Pakistan.
Sensitivity analysis and bifurcation analysis are closely related to each other. In sensitivity analysis, especially global sensitivity analysis the effects of input parameter spaces on output quantities of interest are studied. On the other hand, in bifurcation analysis the critical points within feasible regions of parameters are detected where the long-term dynamics changes qualitatively. Prior to bifurcation analysis, it is important to identify the bifurcation parameters. In complex and computationally expensive problems which consist plenty of uncertain parameters, it is essential to find a set of bifurcation parameters before bifurcation analysis. Global sensitivity analysis is a powerful tool to identify the bifurcation parameters which contribute most on output uncertainty. Global sensitivity analysis is the first step toward bifurcation analysis which helps in dimension reduction during bifurcation analysis. As an example, in this chapter, a multi compartment, lumped-parameter model of an arm artery is considered and global sensitivity analysis (Sobol’s method) is applied to identify the bifurcation parameters of the arm arteries.
Part of the book: Complexity in Biological and Physical Systems