Onset Of Spatiotemporal Chaos Research Articles

Alternation of Defects and Phase Turbulence Induces Extreme Events in an Extended Microcavity Laser.

Out-of-equilibrium systems exhibit complex spatiotemporal behaviors when they present a secondary bifurcation to an oscillatory instability. Here, we investigate the complex dynamics shown by a pulsing regime in an extended, one-dimensional semiconductor microcavity laser whose cavity is composed by integrated gain and saturable absorber media. This system is known to give rise experimentally and theoretically to extreme events characterized by rare and high amplitude optical pulses following the onset of spatiotemporal chaos. Based on a theoretical model, we reveal a dynamical behavior characterized by the chaotic alternation of phase and amplitude turbulence. The highest amplitude pulses, i.e., the extreme events, are observed in the phase turbulence zones. This chaotic alternation behavior between different turbulent regimes is at contrast to what is usually observed in a generic amplitude equation model such as the Ginzburg–Landau model. Hence, these regimes provide some insight into the poorly known properties of the complex spatiotemporal dynamics exhibited by secondary instabilities of an Andronov–Hopf bifurcation.

Spatiotemporal and synchronous chaos in accumulated coupled map lattice

The onset of spatiotemporal chaos in coupled map lattice (CML) with a new coupling scheme called accumulated CML is studied in this paper. A rigorous proof of the existence of chaos in the sense of Li–Yorke is presented. Also the range of the coupling strength in which global synchronization can be obtained is calculated by stability analysis of the synchronized state. Finally, the positivity of Lyapunov exponents confirms the existence of chaos.

Spatiotemporal chaos in sine-Gordon systems subjected to wave fields: Onset and suppression

The onset of spatiotemporal chaos in a damped sine-Gordon system subjected to a plane wave field as well as its suppression by an additional small-amplitude plane wave field are proposed theoretically and confirmed numerically. The relevance of these findings in the context of nonlinear magnetization waves is discussed.

Onset of spatiotemporal chaos in a nonlinear system

We describe the onset of spatiotemporal chaos in a spatially extended nonlinear dynamical system as a result of the loss of transversal stability of an invariant manifold representing a spatially homogeneous and temporally chaotic state. The onset of spatiotemporal chaos is characterized by the switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency.

Onset of spatiotemporal chaos in damped anharmonically driven sine-Gordon systems

The onset is demonstrated of spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping of a sinusoidal force. After introducing soliton collective coordinates, Melnikov’s method is applied to the resulting effective equation of motion to deduce the parameter-space regions of the ac force where chaotic instabilities are induced. The analysis reveals that the chaotic threshold amplitude when altering solely the pulse shape presents a minimum when the transmitted impulse is maximal, the remaining parameters being held constant. The universality of the results is shown by studying the behaviour of the Lyapunov exponent from a simple recursion relation which models an unstable limit cycle. Computer simulations of the sine-Gordon system show good agreement with the theoretical predictions. Additionally, it is found that the reshaping-induced order ↔ chaos route is especially rich, including transitions from a two-breather state to a spatially uniform, periodic oscillatory state. The appearance of this spatially uniform state is explained by means of geometrical resonance analysis.

Control of Growth and Morphology of a Crystal Surface by Induced Spatio-Temporal Oscillations of Surface Temperature

ABSTRACTThis paper presents the model for pattern formation in the course of thermodynamically stable and unstable crystal growth from vapor phase, which is influenced by rapid spatio-temporal variations of substrate and film temperature. In the model, such variations result from the interference heating of a substrate by weak pulsed laser beams. In the thermodynamically stable case the surface relaxational dynamics is influenced by surface diffusion mass transport from hot to cold regions of a substrate; this leads to accumulation of mass in cold regions and depletion in hot regions. In the thermodynamically unstable case the underlying faceting (spinodal) instability coupled to diffusion mass fluxes from hot to cold regions leads to formation of pyramidal surface structures. The scale of stationary coarsened structure increases as the separation distance of the adjacent interference fringes decreases (relative to the intrinsic faceting wave length, which is determined by the balance between the corner regularization energies and the surface energy anisotropy). On the other hand, the coarsening rates decrease with decreasing the separation distance, at least at particular typical deposition strength. The deposition strength and the separation distance of the interference fringes determine the transient and stationary pattern shape. By effectively redistributing adatoms on a substrate through the enhanced, spatially inhomogeneous diffusion, the interference heating mechanism delays, for large separation distances, the onset of spatiotemporal chaos as the growth rate increases.

Turing Instability Leads Oscillatory Systems to Spatiotemporal Chaos

We present that Turing instability can lead oscillatory reaction-diffusion (RD) systems to spatiotemporal chaos instead of spatially periodic steady states. Similar onset of spatiotemporal chaos was discovered in an equation describing seismic waves. We demonstrate that the seismic equation can be derived from a certain class of oscillatory RD systems in the neighborhood of a codimension-two Turing-Benjamin-Feir point. Also, we show numerical studies of reduced equations and discuss robustness of this spatiotemporal chaos.

Accumulations of T-points in a model for solitary pulses in an excitable reaction–diffusion medium

We consider a family of differential equations that describes traveling waves in a reaction–diffusion equation modeling oxidation of carbon oxide on a platinum surface, near the onset of spatio-temporal chaos. The organizing bifurcation for the bifurcation structure with small carbon oxide pressures, turns out to be a codimension 3 bifurcation involving a homoclinic orbit to an equilibrium undergoing a transcritical bifurcation. We show how infinitely many T-point bifurcations of multi loop heteroclinic cycles occur in the unfolding.

Scarred patterns in surface waves.

Surface wave patterns are investigated experimentally in a system geometry that has become a paradigm of quantum chaos: the stadium billiard. Linear waves in bounded geometries for which classical ray trajectories are chaotic are known to give rise to scarred patterns. Here, we utilize parametrically forced surface waves (Faraday waves), which become progressively nonlinear beyond the wave instability threshold, to investigate the subtle interplay between boundaries and nonlinearity. Only a subset (three main types) of the computed linear modes of the stadium are observed in a systematic scan. These correspond to modes in which the wave amplitudes are strongly enhanced along paths corresponding to certain periodic ray orbits. Many other modes are found to be suppressed, in general agreement with a prediction by Agam and Altshuler based on boundary dissipation and the Lyapunov exponent of the associated orbit. Spatially asymmetric or disordered (but time-independent) patterns are also found even near onset. As the driving acceleration is increased, the time-independent scarred patterns persist, but in some cases transitions between modes are noted. The onset of spatiotemporal chaos at higher forcing amplitude often involves a nonperiodic oscillation between spatially ordered and disordered states. We characterize this phenomenon using the concept of pattern entropy. The rate of change of the patterns is found to be reduced as the state passes temporarily near the ordered configurations of lower entropy. We also report complex but highly symmetric (time-independent) patterns far above onset in the regime that is normally chaotic.

Spatiotemporal chaos and effective stochastic dynamics for a near-integrable nonlinear system

We address (i) the onset of spatiotemporal chaos (STC) induced by the hyperbolic structure in a weakly perturbed nonlinear Schrödinger equation, and (ii) its effective stochastic dynamics (ESD). We obtain the following new results: (1) a very small number ( two for our system) of linearly unstable modes is sufficient to trigger the onset of STC as characterized by an exponential decay in space of the mutual information; (2) the construction of the ESD needs only temporal chaos, in contrast to the requirement of full STC as usually believed.

Pulse bifurcation and transition to spatiotemporal chaos in an excitable reaction-diffusion model

We address the stability of solitary pulses as well as some other traveling structures near the onset of spatiotemporal chaos in a two-species reaction-diffusion model describing the oxidation of CO on a Pt(1 1 0) surface in one spatial dimension. First, the boundary of the existence region of stable pulses is explored by means of numerical integration of the reaction-diffusion equations. The partial differential equations (PDEs) of the model are next reduced to a set of ordinary differential equations (ODEs) by the introduction of a moving frame and a detailed analysis of traveling wave solutions and their bifurcations is presented. The results are then compared to findings in numerical simulations and stability computations in the full PDE. The solutions of the ODE are organized around a codimension-2 global bifurcation from which two branches of homoclinic orbits corresponding to solitary pulse solutions in the PDE originate. This bifurcation mediates a change in the dynamics of the excitable medium, as seen in numerical simulations, from a regime dominated by stable pulses and wavetrains traveling with constant shape and speed to spatiotemporally chaotic dynamics. We also find a branch of heteroclinic orbits corresponding to fronts in the PDE. Even though these fronts are found to be unstable for the PDE, their spatial signature is frequently observed locally as part of the spatiotemporally chaotic profiles obtained by direct numerical simulation.

Dynamics of the nonlinear modulational instability in optical fibers

We study the nonlinear evolution in optical fibers of a modulationally unstable continuous wave. We find that a good description of the propagation can be analytically obtained by a simple truncated three-wave model. The dynamic viewpoint may give an important physical insight in different processes, such as frequency conversion of modulated signals, all-optical generation of temporal codes, and the onset of spatiotemporal chaos.