Crisis-induced intermittent bursting in reaction-diffusion chemical systems

Nonlinear dynamics and intermittency in a turbulent reacting wake with density ratio as bifurcation parameter

The flame or flow behavior of a turbulent reacting wake is known to be fundamentally different at high and low values of flame density ratio (ρ_{u}/ρ_{b}), as the flow transitions from globally stable to unstable. This paper analyzes the nonlinear dynamics present in a bluff-body stabilized flame, and identifies the transition characteristics in the wake as ρ_{u}/ρ_{b} is varied over a Reynolds number (based on the bluff-body lip velocity) range of 1000-3300. Recurrence quantification analysis (RQA) of the experimentally obtained time series of the flame edge fluctuations reveals that the time series is highly aperiodic at high values of ρ_{u}/ρ_{b} and transitions to increasingly correlated or nearly periodic behavior at low values. From the RQA of the transverse velocity time series, we observe that periodicity in the flame oscillations are related to periodicity in the flow. Therefore, we hypothesize that this transition from aperiodic to nearly periodic behavior in the flame edge time series is a manifestation of the transition in the flow from globally stable, convective instability to global instability as ρ_{u}/ρ_{b} decreases. The recurrence analysis further reveals that the transition in periodicity is not a sudden shift; rather it occurs through an intermittent regime present at low and intermediate ρ_{u}/ρ_{b}. During intermittency, the flow behavior switches between aperiodic oscillations, reminiscent of a globally stable, convective instability, and periodic oscillations, reminiscent of a global instability. Analysis of the distribution of the lengths of the periodic regions in the intermittent time series and the first return map indicate the presence of type-II intermittency.

Intermittent explosions of dissipative solitons and noise-induced crisis

Dissipative solitons show a variety of behaviors not exhibited by their conservative counterparts. For instance, a dissipative soliton can remain localized for a long period of time without major profile changes, then grow and become broader for a short time-explode-and return to the original spatial profile afterward. Here we consider the dynamics of dissipative solitons and the onset of explosions in detail. By using the one-dimensional complex Ginzburg-Landau model and adjusting a single parameter, we show how the appearance of explosions has the general signatures of intermittency: the periods of time between explosions are irregular even in the absence of noise, but their mean value is related to the distance to criticality by a power law. We conjecture that these explosions are a manifestation of attractor-merging crises, as the continuum of localized solitons induced by translation symmetry becomes connected by short-lived trajectories, forming a delocalized attractor. As additive noise is added, the extended system shows the same scaling found by low-dimensional systems exhibiting crises [J. Sommerer, E. Ott, and C. Grebogi, Phys. Rev. A 43, 1754 (1991)], thus supporting the validity of the proposed picture.

Nonlinear effects on Turing patterns: time oscillations and chaos

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems.

Chaotically spiking attractors in suspended-mirror optical cavities

A high-finesse suspended-mirror Fabry-Perot cavity is experimentally studied in a regime where radiation pressure and photothermal effect are both relevant. The competition between these phenomena, operating at different timescales, produces unobserved dynamical scenarios where an initial Hopf instability is followed by the birth of small-amplitude chaotic attractors that erratically but deterministically trigger optical spikes. The observed dynamical regimes are well reproduced by a detailed physical model of the system.

Complex evolution of spike patterns during burst propagation through feed-forward networks

Stable signal transmission is crucial for information processing by the brain. Synfire-chains, defined as feed-forward networks of spiking neurons, are a well-studied class of circuit structure that can propagate a packet of single spikes while maintaining a fixed packet profile. Here, we studied the stable propagation of spike bursts, rather than single spike activities, in a feed-forward network of a general class of excitable bursting neurons. In contrast to single spikes, bursts can propagate stably without converging to any fixed profiles. Spike timings of bursts continue to change cyclically or irregularly during propagation depending on intrinsic properties of the neurons and the coupling strength of the network. To find the conditions under which bursts lose fixed profiles, we propose an analysis based on timing shifts of burst spikes similar to the phase response analysis of limit-cycle oscillators.

Chaos and intermittent bursting in a reaction-diffusion process

Karhunen-Loeve decomposition is done on a chaotic spatio-temporal solution obtained from a nonlinear reaction-diffusion model of a chemical system simulating a chemical process in an open Couette-flow reactor. Using a Galerkin projection of the dominant Karhunen-Loeve modes back onto the nonlinear partial differential system, we obtain an ordinary differential equation model of the same process. Major features such as intermittent and chaotic bursting of the nonlinear process as well as the mechanism of transition to chaos are shown to exist in the low-dimensional model as well as the PDE model. From the low-dimensional model the onset of intermittent bursts followed by small amplitude oscillations is shown to arise due to a sequence of saddle-node bifurcations.