Nonchaos-Mediated Mixed-Mode Oscillations in an Enzyme Reaction System

Complexity in subnetworks of a peroxidase-oxidase reaction model

The peroxidase-oxidase (PO) reaction is a paradigmatic (bio)chemical system well suited to study the organization and stability of self-sustained oscillatory phases typically present in nonlinear systems. The PO reaction can be simulated by the state-of-the-art Bronnikova-Fedkina-Schaffer-Olsen model involving ten coupled ordinary differential equations. The complex and dynamically rich distribution of self-sustained oscillatory stability phases of this model was recently investigated in detail. However, would it be possible to understand aspects of such a complex model using much simpler models? Here, we investigate stability phases predicted by three simple four-variable subnetworks derived from the complete model. While stability diagrams for such subnetworks are found to be distorted compared to those of the complete model, we find them to surprisingly preserve significant features of the original model as well as from the experimental system, e.g., period-doubling and period-adding scenarios. In addition, return maps obtained from the subnetworks look very similar to maps obtained in the experimental system under different conditions. Finally, two of the three subnetwork models are found to exhibit quint points, i.e., recently reported singular points where five distinct stability phases coalesce. We also provide experimental evidence that such quint points are present in the PO reaction.

The onset of dissipative chaos driven by nonequilibrium conditions

Dissipative chaos appears widely in various nonequilibrium systems; however, it is not clear how dissipative chaos originates from nonequilibrium. We discuss a framework based on the potential-flux approach to study chaos from the perspective of nonequilibrium dynamics. In this framework, chaotic systems possess a wide basin on the potential landscape, in which the rotational flux dominates the system dynamics, and chaos occurs with the appearance of this basin. In contrast, the probability flux is particularly associated with the detailed balance-breaking in nonequilibrium systems. This implies that the appearance of dissipative chaos is driven by nonequilibrium conditions.

Complexity of a peroxidase-oxidase reaction model

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 a state-of-the-art model of the peroxidase-oxidase reaction. Using the model, we report systematic numerical experiments exploring the impact of changing the enzyme concentration on the dynamics of the reaction. Specifically, we report high-resolution phase diagrams predicting and describing how the reaction unfolds over a quite extended range of enzyme concentrations. Surprisingly, such diagrams reveal that the enzyme concentration has a huge impact on the reaction evolution. The highly intricate dynamical behaviours predicted here are difficult to establish theoretically due to the total absence of an adequate framework to solve nonlinearly coupled differential equations. But such behaviours may be validated experimentally.

Chaos in the peroxidase-oxidase oscillator

The peroxidase-oxidase (PO) reaction involves the oxidation of reduced nicotinamide adenine dinucleotide by molecular oxygen. When both reactants are supplied continuously to a reaction mixture containing the enzyme and a phenolic compound, the reaction will exhibit oscillatory behavior. In fact, the reaction exhibits a zoo of dynamical behaviors ranging from simple periodic oscillations to period-doubled and mixed mode oscillations to quasiperiodicity and chaos. The routes to chaos involve period-doubling, period-adding, and torus bifurcations. The dynamic behaviors in the experimental system can be simulated by detailed semiquantitative models. Previous models of the reaction have omitted the phenolic compound from the reaction scheme. In the current paper, we present new experimental results with the oscillating PO reaction that add to our understanding of its rich dynamics, and we describe a new variant of a previous model, which includes the chemistry of the phenol in the reaction mechanism. This new model can simulate most of the experimental behaviors of the experimental system including the new observations presented here. For example, the model reproduces the two main routes to chaos observed in experiments: (i) a period-doubling scenario, which takes place at low pH, and a period-adding scenario involving mixed mode oscillations (MMOs), which occurs at high pH. Our simulations suggest alternative explanations for the pH-sensitivity of the dynamics. We show that the MMO domains are separated by narrow parameter regions of chaotic behavior or quasiperiodicity. These regions start as tongues of secondary quasiperiodicity and develop into strange attractors through torus breakdown.

A numerical investigation of the effect of external resistance and applied potential on the distribution of periodicity and chaos in the anodic dissolution of nickel

Low density, elongation, and suppression of the shrimp-like structures in the resistance-potential phase diagrams have been observed in the oscillatory dissolution of nickel.

Size- and position-dependent bifurcations of chemical microoscillators in confined geometries

The present theoretical study deals with microparticles (beads) that contain an immobilized Belousov-Zhabotinsky (BZ) reaction catalyst. In the theoretical experiment, a BZ bead is immersed in a small water droplet that contains all of the BZ reaction reagents but no catalyst. Such heterogeneous reaction-diffusion BZ systems with the same BZ reactant concentrations demonstrate various dynamic modes, including steady state and low-amplitude, high-amplitude, and mixed-mode oscillations (MMOs). The emergence of such dynamics depends on the sizes of the bead and water droplet, as well as on the location of the bead inside the droplet. MMO emergence is explained by time-delayed positive feedback in combination with a canard phenomenon. If two identical BZ beads are immersed in the same droplet, many different dynamic modes including chaos are observed.

Impact of predator dormancy on prey-predator dynamics

The impact of predator dormancy on the population dynamics of phytoplankton-zooplankton in freshwater ecosystems is investigated using a simple model including dormancy, a strategy to avoid extinction. In addition to recently reported chaos-mediated mixed-mode oscillations, as the carrying capacity grows, we find surprisingly wide phases of nonchaos-mediated mixed-mode oscillations to be present well before the onset of chaos in the system. Nonchaos-mediated cascades display spike-adding sequences, while chaos-mediated cascades show spike-doubling. A host of braided periodic phases with exotic shapes is found embedded in a region of control parameters dominated by chaotic oscillations. We describe the organization of these complicated phases and show how they are interconnected and how their complexity unfolds as control parameters change. The novel nonchaos-mediated phases are found to be large and stable, even for low carrying capacity.

Self-organization of pulsing and bursting in a CO2 laser with opto-electronic feedback

We report a detailed investigation of the stability of a CO2 laser with feedback as described by a six-dimensional rate-equations model which provides satisfactory agreement between numerical and experimental results. We focus on experimentally accessible parameters, like bias voltage, feedback gain, and the bandwidth of the feedback loop. The impact of decay rates and parameters controlling cavity losses are also investigated as well as control planes which imply changes of the laser physical medium. For several parameter combinations, we report stability diagrams detailing how laser spiking and bursting is organized over extended intervals. Laser pulsations are shown to emerge organized in several hitherto unseen regular and irregular phases and to exhibit a much richer and complex range of behaviors than described thus far. A significant observation is that qualitatively similar organization of laser spiking and bursting can be obtained by tuning rather distinct control parameters, suggesting the existence of unexpected symmetries in the laser control space.

Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model

We report some regular organizations of stability phases discovered among self-sustained oscillations of a biochemical oscillator. The signature of such organizations is a nested arithmetic progression in the number of spikes of consecutive windows of periodic oscillations. In one of them, there is a main progression of windows whose consecutive number of spikes differs by one unit. Such windows are separated by a secondary progression of smaller windows whose number of spikes differs by two units. Another more complex progression involves a fan-like nested alternation of stability phases whose number of spikes seems to grow indefinitely and to accumulate methodically in cycles. Arithmetic progressions exist abundantly in several control parameter planes and can be observed by tuning just one among several possible rate constants governing the enzyme reaction.