scholarly journals Complexity of a Peroxidase-Oxidase Reaction Model

2021 ◽  
Author(s):  
Jason Gallas ◽  
Marcus Hauser ◽  
Lars Folke Olsen
Keyword(s):  
Chemical Reaction ◽  
Mixed Mode ◽  
Period Doubling ◽  
Reaction Model ◽  
Chaotic Behaviour ◽  
Mixed Mode Oscillations ◽  
Oscillating Reaction ◽  
Oxidase Reaction

The peroxidase-oxidase oscillating reaction was the first (bio)chemical reaction to show chaotic behaviour. The reaction is rich in bifurcation scenarios, from period-doubling to peak-adding mixed mode oscillations. Here, we study...

Chaos via mixed-mode oscillations

1991 ◽  
Vol 337 (1646) ◽  
pp. 291-298 ◽  
Keyword(s):  
Mixed Mode ◽  
Phase Locking ◽  
Period Doubling ◽  
Specific Model ◽  
Dynamical Behaviour ◽  
Object A ◽  
Mixed Mode Oscillations ◽  
Catalysed Oxidation ◽  
Periodic State ◽  
Peroxidase Enzyme

The route by which chaos arises from mixed-mode periodic states in a model of the peroxidase enzyme catalysed oxidation of NADH is described. The specific model studied displays a rich variety of exotic dynamical behaviour including simple oscillations, quasiperiodicity, bistability between periodic states, complex periodic oscillations (including the mixed-mode type) and chaos. The route to chaos in this system involves a torus attractor which becomes destabilized and breaks up into a fractal object, a strange attractor. The mixed-mode states correspond to phase-locking on this fractal attractor and are arranged in staircases according to the complexity of the state. In this paper, we investigate the sequence leading from a mixed-mode periodic state to a chaotic one in the staircase region and find a familiar cascade of period-doubling bifurcations, which finally culminate in chaos.

Period doubling and other complex bifurcations in non-isothermal chemical systems

1990 ◽  
Vol 332 (1624) ◽  
pp. 51-68 ◽  
Keyword(s):  
Mixed Mode ◽  
Period Doubling ◽  
Heat Rate ◽  
Oscillatory Behaviour ◽  
Chemical Heat ◽  
Experimental Conditions ◽  
Chemical Systems ◽  
Mixed Mode Oscillations ◽  
Self Heating ◽  
Thermal Feedback

Chemical feedback in the form of chain-branching or autocatalysis can give rise to oscillatory behaviour in very simple models involving only two variables. Many chemical reactions are also exothermic. This chemical heat release can give rise to self-heating and hence to thermal feedback, where the temperature varies as well as the concentrations. When chemical and thermal feedback are coupled, the range of responses that can be observed are increased dramatically. These features are demonstrated through the simple non-isothermal autocatalator scheme p-> A rate = A + 2B-> 3B rate = k1 2, A-^ B rate = kza, C + heat rate = At its simplest, the reaction can be steady or can show simple period-1 oscillations. More complex oscillations, with higher periodicity appear as the experimental conditions are varied, with period doubling, mixed-mode oscillations and aperiodicity (chemical chaos).

Symmetric Fold/Super-Hopf Bursting, Chaos and Mixed-Mode Oscillations in Pernarowski Model of Pancreatic Beta-Cells

2016 ◽  
Vol 26 (09) ◽  
pp. 1630022 ◽  
Author(s):  
Haniyeh Fallah
Keyword(s):  
Blood Glucose ◽  
Blood Glucose Level ◽  
Beta Cells ◽  
Pancreatic Beta Cells ◽  
Mixed Mode ◽  
Current System ◽  
Period Doubling ◽  
Slow Manifold ◽  
Mixed Mode Oscillations ◽  
Route To Chaos

Pancreatic beta-cells produce insulin to regularize the blood glucose level. Bursting is important in beta cells due to its relation to the release of insulin. Pernarowski model is a simple polynomial model of beta-cell activities indicating bursting oscillations in these cells. This paper presents bursting behaviors of symmetric type in this model. In addition, it is shown that the current system exhibits the phenomenon of period doubling cascades of canards which is a route to chaos. Canards are also observed symmetrically near folds of slow manifold which results in a chaotic transition between [Formula: see text] and [Formula: see text] spikes symmetric bursting. Furthermore, mixed-mode oscillations (MMOs) and combination of symmetric bursting together with MMOs are illustrated during the transition between symmetric bursting and continuous spiking.

Mixed-Mode Oscillations and Twin Canard Orbits in an Autocatalytic Chemical Reaction

2017 ◽  
Vol 16 (4) ◽  
pp. 2165-2195 ◽  
Author(s):  
Cris R. Hasan ◽  
Bernd Krauskopf ◽  
Hinke M. Osinga
Keyword(s):  
Chemical Reaction ◽  
Mixed Mode ◽  
Mixed Mode Oscillations

Mixed-mode oscillations in a homogeneouspH-oscillatory chemical reaction system

2008 ◽  
Vol 18 (1) ◽  
pp. 015102 ◽  
Author(s):  
Daniel Bakeš ◽  
Lenka Schreiberová ◽  
Igor Schreiber ◽  
Marcus J. B. Hauser
Keyword(s):  
Chemical Reaction ◽  
Mixed Mode ◽  
Reaction System ◽  
Mixed Mode Oscillations ◽  
Chemical Reaction System ◽  
Oscillatory Chemical ◽  
Oscillatory Chemical Reaction

scholarly journals The geometry of mixed-mode oscillations in the Olsen model for the Peroxidase-Oxidase reaction

2009 ◽  
Vol 2 (4) ◽  
pp. 807-827 ◽  
Author(s):  
Mathieu Desroches ◽  
◽  
Bernd Krauskopf ◽  
Hinke M. Osinga
Keyword(s):  
Mixed Mode ◽  
Mixed Mode Oscillations ◽  
Oxidase Reaction

Mixed-mode oscillations and chaos in return maps of an oscillatory chemical reaction

2015 ◽  
Vol 89 (13) ◽  
pp. 2349-2358 ◽  
Author(s):  
S. N. Blagojević ◽  
Ž. Čupić ◽  
A. Ivanović-Šašić ◽  
Lj. Kolar-Anić
Keyword(s):  
Chemical Reaction ◽  
Mixed Mode ◽  
Mixed Mode Oscillations ◽  
Return Maps ◽  
Oscillatory Chemical ◽  
Oscillatory Chemical Reaction

Mixed Mode Oscillations (MMOs)

2021 ◽  
Author(s):  
Zdzislaw Trzaska
Keyword(s):  
Mixed Mode ◽  
Mixed Mode Oscillations

scholarly journals Development of an Uncertainty Quantification Predictive Chemical Reaction Model for Syngas Combustion

2017 ◽  
Vol 31 (3) ◽  
pp. 2274-2297 ◽  
Author(s):  
N. A. Slavinskaya ◽  
M. Abbasi ◽  
J. H. Starcke ◽  
R. Whitside ◽  
A. Mirzayeva ◽  
...  
Keyword(s):  
Uncertainty Quantification ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Syngas Combustion ◽  
Chemical Reaction Model
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