scholarly journals Oscillations in Planar Deficiency-One Mass-Action Systems

2021 ◽  
Author(s):  
Balázs Boros ◽  
Josef Hofbauer
Keyword(s):  
Limit Cycles ◽  
Mass Action ◽  
Positive Equilibrium ◽  
Oscillatory Behaviour ◽  
Action Systems ◽  
Action System ◽  
Globally Stable

AbstractWhereas the positive equilibrium of a planar mass-action system with deficiency zero is always globally stable, for deficiency-one networks there are many different scenarios, mainly involving oscillatory behaviour. We present several examples, with centers or multiple limit cycles.

scholarly journals Complex-balanced equilibria of generalized mass-action systems: necessary conditions for linear stability

2020 ◽  
Vol 17 (1) ◽  
pp. 442-459
Author(s):  
Balázs Boros ◽  
◽  
Stefan Müller ◽  
Georg Regensburger ◽  
Keyword(s):  
Linear Stability ◽  
Necessary Conditions ◽  
Mass Action ◽  
Action Systems

scholarly journals Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems

2005 ◽  
Vol 40 (6) ◽  
pp. 1361-1382 ◽  
Author(s):  
Karin Gatermann ◽  
Markus Eiswirth ◽  
Anke Sensse
Keyword(s):  
Graph Theory ◽  
Mass Action ◽  
Hopf Bifurcations ◽  
Toric Ideals ◽  
Action Systems

Limit Cycles in a Class of Quartic Kolmogorov Model with Three Positive Equilibrium Points

2015 ◽  
Vol 25 (06) ◽  
pp. 1550080 ◽  
Author(s):  
Chaoxiong Du ◽  
Yirong Liu ◽  
Qi Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Equilibrium Points ◽  
Positive Equilibrium ◽  
Bifurcation Problem ◽  
Kolmogorov Model ◽  
Limit Cycle Bifurcation ◽  
Perturbed Model

Limit cycle bifurcation problem of Kolmogorov model is interesting and significant both in theory and applications. In this paper, we will focus on investigating limit cycles for a class of quartic Kolmogorov model with three positive equilibrium points. Perturbed model can bifurcate three small limit cycles near (1, 2) or (2, 1) under a certain condition and can bifurcate one limit cycle near (1, 1). In addition, we have given some examples of simultaneous Hopf bifurcation and the structure of limit cycles bifurcated from three positive equilibrium points. The limit cycle bifurcation problem for Kolmogorov model with several positive equilibrium points are less seen in published references. Our result is good and interesting.

QUALITATIVE ANALYSIS FOR THE MERKIN ENZYME REACTION SYSTEM

2002 ◽  
Vol 10 (02) ◽  
pp. 167-182
Author(s):  
YUQUAN WANG ◽  
ZUORUI SHEN
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycles ◽  
Local Stability ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Reaction System ◽  
Enzyme Reaction ◽  
Qualitative Theory ◽  
Positive Equilibrium ◽  
Hopf Bifurcations

Applying qualitative theory and Hopf bifurcation theory, we detailedly discuss the Merkin enzyme reaction system, and the sufficient conditions derived for the global stability of the unique positive equilibrium, the local stability of three equilibria and the existence of limit cycles. Meanwhile, we show that the Hopf bifurcations may occur. Using MATLAB software, we present three examples to simulate these conclusions in this paper.

Kinetic investigation of complex pseudo mass action systems by use of the pulse method

1980 ◽  
Vol 58 (4) ◽  
pp. 513-516 ◽  
Author(s):  
Erhard G. Christoffel ◽  
Indarto T. Surjo ◽  
Karl-H. Robschlager
Keyword(s):  
Pulse Method ◽  
Mass Action ◽  
Kinetic Investigation ◽  
Action Systems
Sign in / Sign up

Export Citation Format

Share Document