Complexity of a peroxidase–oxidase reaction model

Abstract

The peroxidase–oxidase reaction was he first (bio)chemical reaction to show chaotic dynamics. Here, we show that the rich complex dynamics observed in a detailed model of the reaction changes dramatically with changes in enzyme concentration.

Complexity in subnetworks of a peroxidase–oxidase reaction model

“…Such diagrams are then compared with similar diagrams of the original BFSO model. 29,36 The isospike stability diagrams of the tree subnetwork models reveal complex periodic structures which enlighten and explain previous experimental observations in the PO reaction, that is bifurcations and return maps. Two of the subnetworks also predict the existence of of the recently reported quint points, 10,[41][42][43] that is singular points where five distinct stability phases coalesce.…”

“…One example is the surprising and unpredictable complex behavior induced by changes in the enzyme concentration. 36 In 2006, Sensse et al 37 succeeded in reducing the BFSO model to a 6-variable model and, subsequently, to three simpler 4variable subnetwork models, that could be studied individually. The three 4-variable subnetworks so obtained have strong similarities to 3-variable extended activator-inhibitor networks introduced earlier.…”

Chirality detected in Hartley’s electronic oscillator

“…In experiments, C G D may be simulated using operational amplifiers. The classification is done using isospike stability diagrams [10][11][12][13][14][15][16][17][18], the flow version of the isoperiodic stability diagrams commonly used for maps [19][20][21][22]24]. Briefly, for a given set of parameters, we numerically integrate the equations of motion recording the number of spikes per period for all periodic oscillations.…”

“…To count oscillation spikes is easy to do in a very reliable way. The fruitful isospike technique to classify complex oscillations is discussed in-depth in recent literature [10][11][12][13][14][15][16][17][18].…”

Ubiquity of ring structures in the control space of complex oscillators

“…We computed two types of stability diagrams: the standard Lyapunov diagrams 18 and the so-called isospike diagrams. [19][20][21][22][23][24][25][26][27][28][29] Here, isospike diagrams are constructed by painting each point of the control plane with colors reflecting the number of spikes (local maxima) per period of the periodic oscillations and assigning some specific color to record nonperiodic oscillations. Computationally, isospike diagrams are a much simpler and less costly way to obtain all the information of Lyapunov diagrams, plus a significant enhancement: instead of lumping together all periodic oscillations into a single-phase as Lyapunov diagrams do, isospike diagrams classify oscillations by explicitly displaying the number of spikes per period for every individual oscillation.…”