Bifurcation analysis of bistable and oscillatory dynamics in biological networks using the root‐locus method. Issue 6 (1st December 2019)

• Record Type: Journal Article
• Authors: Avcu, Neslihan; Güzeliş, Cüneyt
• Is Part Of: IET systems biology. Volume 13:Issue 6(2019)
• Page Start: 333
• Page End: 345
• Publication Date: 2019-12-01
• Subjects: oscillations -- curve fitting -- differential equations -- bifurcation -- genetics -- nonlinear dynamical systems; nonlinearities -- reaction kinetics -- root‐locus‐based bifurcation analysis method -- complex dynamics -- exact parameter regions -- dynamical behaviour -- equilibrium dynamics -- studied gene regulatory networks -- p53 gene network -- bistable dynamics -- oscillatory dynamics -- biological networks -- root‐locus method -- biological systems -- ordinary differential equation models; Systems biology -- Periodicals; Cell physiology -- Periodicals; Biological systems -- Mathematical models -- Periodicals; Genetics -- Mathematical models -- Periodicals; Computational biology -- Periodicals; 573
• DOI: 10.1049/iet-syb.2019.0043
• Languages: English
• ISSNs: 1751-8849

Abstract

Abstract : Most of the biological systems including gene regulatory networks can be described well by ordinary differential equation models with rational non‐linearities. These models are derived either based on the reaction kinetics or by curve fitting to experimental data. This study demonstrates the applicability of the root‐locus‐based bifurcation analysis method for studying the complex dynamics of such models. The effectiveness of the bifurcation analysis in determining the exact parameter regions in each of which the system shows a certain dynamical behaviour, such as bistability, oscillation, and asymptotically equilibrium dynamics is shown by considering two mostly studied gene regulatory networks, namely Gardner's genetic toggle switch and p53 gene network possessing two‐phase (mono‐stable/oscillation) dynamics.