Origin of bursting oscillations in an enzyme model reaction system

Synchronous behaviour of two interacting oscillatory systems undergoing quasiperiodic route to chaos

Thermoacoustic instability, caused by a positive feedback between the unsteady heat release and the acoustic field in a combustor, is a major challenge faced in most practical combustors such as those used in rockets and gas turbines. We employ the synchronization theory for understanding the coupling between the unsteady heat release and the acoustic field of a thermoacoustic system. Interactions between coupled subsystems exhibiting different collective dynamics such as periodic, quasiperiodic, and chaotic oscillations are addressed. Even though synchronization studies have focused on different dynamical states separately, synchronous behaviour of two coupled systems exhibiting a quasiperiodic route to chaos has not been studied. In this study, we report the first experimental observation of different synchronous behaviours between two subsystems of a thermoacoustic system exhibiting such a transition as reported in Kabiraj et al. [Chaos 22, 023129 (2012)]. A rich variety of synchronous behaviours such as phase locking, intermittent phase locking, and phase drifting are observed as the dynamics of such subsystem change. The observed synchronization behaviour is further characterized using phase locking value, correlation coefficient, and relative mean frequency. These measures clearly reveal the boundaries between different states of synchronization.

Nonlinear Dynamics in the Uncatalyzed Bromate–Pyrocatechol Reaction

Spontaneous chemical oscillations are uncovered in the uncatalyzed bromate–pyrocatechol reaction conducted in a stirred batch reactor. Phase diagrams show that the oscillatory behavior is more sensitive to the ratio of [bromate]/[pyrocatechol] than their actual concentrations. The long induction time observed in the system is insensitive to the initial presence of brominated pyrocatechol species. Quenching experiments illustrate that the studied chemical oscillator is both bromide and radical controlled. In addition, this new uncatalyzed bromate oscillator exhibits both light-induced and light-quenched oscillatory behaviors. Preliminary mechanistic characterization with UV/vis absorption method and mass spectrometry suggests the formation of bromo-1,2-benzoquinone through the reaction between pyrocatechol and bromine.

Mixed-mode oscillations and cluster patterns in an electrochemical relaxation oscillator under galvanostatic control

We studied the dynamics of a prototypical electrochemical model, the electro-oxidation of hydrogen in the presence of poisons, under galvanostatic conditions. The lumped system exhibits relaxation oscillations, which develop mixed-mode oscillations (MMOs) for low preset currents. A fast-slow analysis of the homogeneous dynamics reveals that the MMOs arise from a fast oscillating subsystem and a one-dimensional slow manifold. In the spatially extended system, the galvanostatic constraint imposes a synchronizing global coupling that drives the system into cluster patterns. The properties of the cluster patterns (CPs) result from an intricate interplay of the nature of the local oscillators, the global constraint, and a nonlocal coupling through the electrolyte. In particular, we find that the global constraint suppresses small-amplitude oscillations of MMOs and prevents domains oscillating out of phase from occupying equal regions in phase space. The nonlocal coupling causes each individual clustered region to oscillate on a different limit cycle. Typically multistability of CPs is found. Coexisting patterns possess different oscillation periods and a different total fraction in space that occupies the in-phase or out-of-phase state, respectively.

Mixed-mode oscillations in a homogeneous pH-oscillatory chemical reaction system

We examine experimentally a chemical system in a flow-through stirred reactor, which is known to provide large-amplitude oscillations of the pH value. By systematic variation of the flow rate, we find that the system displays hysteresis between a steady state and oscillations, and more interestingly, a transition to chaos involving mixed-mode oscillations. The basic pattern of the measured pH in the mixed-mode regime includes a large-scale peak followed by a series of oscillations on a much smaller scale, which are usually highly irregular and of variable duration. The bifurcation diagram shows that chaos sets in via a period-doubling route observed on the large-amplitude scale, but simultaneously small-amplitude oscillations are involved. Beyond the apparent accumulation of period doubling bifurcations, a mixed-mode regime with irregular oscillations on both scales is observed, occasionally interrupted by windows of periodicity. As the flow rate is further increased, chaos turns into quasiperiodicity and later to a simple small-amplitude periodic regime. Dynamics of selected typical regimes were examined with the tools of nonlinear time-series analysis, which include phase space reconstruction of an attractor and calculation of the maximal Lyapunov exponent. The analysis points to deterministic chaos, which appears via a period doubling route from below and via a route involving quasiperiodicity from above, when the flow rate is varied.

Chaotically spiking canards in an excitable system with 2D inertial fast manifolds

We introduce a new class of excitable systems with two-dimensional fast dynamics that includes inertia. A novel transition from excitability to relaxation oscillations is discovered where the usual Hopf bifurcation is followed by a cascade of period doubled and chaotic small excitable attractors and, as they grow, by a new type of canard explosion where a small chaotic background erratically but deterministically triggers excitable spikes. This scenario is also found in a model for a nonlinear Fabry-Perot cavity with one pendular mirror.