Open AccessDynamics of a delay turbidostat system with contois growth rate
Author(s) -
Yong Yao
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019003
Subject(s) - center manifold , hopf bifurcation , bifurcation , biological applications of bifurcation theory , transcritical bifurcation , mathematics , stability (learning theory) , control theory (sociology) , saddle node bifurcation , bifurcation diagram , pitchfork bifurcation , mathematical analysis , physics , computer science , nonlinear system , control (management) , quantum mechanics , machine learning , artificial intelligence
In this contribution, the dynamic behaviors of a turbidostat model with Contois growth rate and delay are investigated. The qualitative properties of the system are carried out including the stability of the equilibria and the bifurcations. More concretely, we exhibit the transcritical bifurcation by reducing the system without delay to a 1-dimensional system on a center manifold and nd that Hopf bifurcation occurs by choosing the delay as bifurcation parameter. Also, using the normal form theory and the center manifold theorem we determine the direction and stability of the bifurcating periodic solutions induced by the Hopf bifurcation. Finally, numerical simulations are presented to support our theoretical results.