Noise-induced on–off intermittency in mutually coupled semiconductor lasers

Intermittent switches between low-frequency fluctuations and steady-state emission are experimentally observed in two bidirectionally coupled semiconductor lasers subject to common Gaussian noise applied to the laser pump currents. The time series analysis reveals power-law scalings typical for on–off intermittency near its onset, with critical exponents of −1 for the mean turbulent length versus noise intensity and −3/2 for probability distribution of laminar phases versus the laminar length. The same −1 power-law scaling is found by the power spectrum analysis for the signal-to-noise ratio versus the noise intensity.     

On–off intermittent synchronization between two bidirectionally coupled double scroll circuits

In this report the intermittent route from full synchronization to full desynchronization, of two bidirectionally coupled, double-scroll circuits, was experimentally studied. Coupling resistance, between the two circuits, served as the bifurcation parameter, controlling the synchronization. It was shown that the synchronization–desynchronization transition was realized through a regime of incomplete synchronization of the on–off intermittency type.     

Transitions to chaos in squeeze-film dampers

This work reports on a numerical study undertaken to investigate the imbalance response of a rigid rotor supported by squeeze-film dampers. Two types of damper configurations were considered, namely, dampers without centering springs, and eccentrically operated dampers with centering springs. For a rotor fitted with squeeze-film dampers without centering springs, the study revealed the existence of three regimes of chaotic motion. The route to chaos in the first regime was attributed to a sequence of period-doubling bifurcations of the period-1 (synchronous) rotor response. A period-3 (one-third subharmonic) rotor whirl orbit, which was born from a saddle-node bifurcation, was found to co-exist with the chaotic attractor. The period-3 orbit was also observed to undergo a sequence of period-doubling bifurcations resulting in chaotic vibrations of the rotor. The route to chaos in the third regime of chaotic rotor response, which occurred immediately after the disappearance of the period-3 orbit due to a saddle-node bifurcation, was attributed to a possible boundary crisis. The transitions to chaotic vibrations in the rotor supported by eccentric squeeze-film dampers with centering springs were via the period-doubling cascade and type 3 intermittency routes. The type 3 intermittency transition to chaos was due to an inverse period-doubling bifurcation of the period-2 (one-half subharmonic) rotor response. The unbalance response of the squeeze-film-damper supported rotor presented in this work leads to unique non-synchronous and chaotic vibration signatures. The latter provide some useful insights into the design and development of fault diagnostic tools for rotating machinery that operate in highly nonlinear regimes.     

Stochastic Stability of Some Mechanical Systems

We discuss the behavior, for large values of time, of two linear stochastic mechanical systems. The systems are similar mathematically in that they contain a white noise in their parameters. The initial data may be random as well but are independent of white noise. The expected energy is calculated in both cases. It is well known that for free nonstochastic mechanical systems with viscous damping, the energy approaches zero as time increases. We check that this behavior takes place for the stochastic systems under consideration in the case when the initial data are random but the parameters are not. When the parameters contain a random noise the expected energy may be infinite, approach zero, remain bounded, or increase with no bound. This regime is similar to but more interesting than the known regime for the solutions of differential equations with time dependent periodic coefficients that describes the behavior of a mechanical system with characteristics that are periodic functions of time. We give necessary and sufficient conditions for stability of both systems in terms of the structure of the set of roots of an auxiliary equation.     

Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency

In many complex systems the non-linear cooperative dynamics determine the emergence of self-organized, metastable, structures that are associated with a birth–death process of cooperation. This is found to be described by a renewal point process, i.e., a sequence of crucial birth–death events corresponding to transitions among states that are faster than the typical long-life time of the metastable states. Metastable states are highly correlated, but the occurrence of crucial events is typically associated with a fast memory drop, which is the reason for the renewal condition. Consequently, these complex systems display a power-law decay and, thus, a long-range or scale-free behavior, in both time correlations and distribution of inter-event times, i.e., fractal intermittency.The emergence of fractal intermittency is then a signature of complexity. However, the scaling features of complex systems are, in general, affected by the presence of added white or short-term noise. This has been found also for fractal intermittency.In this work, after a brief review on metastability and noise in complex systems, we discuss the emerging paradigm of Temporal Complexity. Then, we propose a model of noisy fractal intermittency, where noise is interpreted as a renewal Poisson process with event rate r_p. We show that the presence of Poisson noise causes the emergence of a normal diffusion scaling in the long-time range of diffusion generated by a telegraph signal driven by noisy fractal intermittency. We analytically derive the scaling law of the long-time normal diffusivity coefficient. We find the surprising result that this long-time normal diffusivity depends not only on the Poisson event rate, but also on the parameters of the complex component of the signal: the power exponent μ of the inter-event time distribution, denoted as complexity index, and the time scale T needed to reach the asymptotic power-law behavior marking the emergence of complexity. In particular, in the range μ < 3, we find the counter-intuitive result that normal diffusivity increases as the Poisson rate decreases.Starting from the diffusivity scaling law here derived, we propose a novel scaling analysis of complex signals being able to estimate both the complexity index μ and the Poisson noise rate r_p.     

Diffusion dynamics near critical bifurcations in a nonlinearly damped pendulum system

We numerically study the diffusion dynamics near critical bifurcations such as sudden widening of the size of a chaotic attractor, intermittency and band-merging of a chaotic attractor in a nonlinearly damped and periodically driven pendulum system. The system is found to show only normal diffusion. Near sudden widening and intermittency crisis power-law variation of diffusion constant with the control parameter ω of the external periodic force f sin ωt is found while linear variation of it is observed near band-merging crisis. The value of the exponent in the power-law relation varies with the damping coefficient and the strength of the added Gaussian white noise.     

Transition to turbulence in coupled maps on hierarchical lattices

General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal intermittency is investigated for these geometries. Critical exponents associated to the onset of turbulence are calculated as functions of the parameters of the systems. No evidence of non-trivial collective behavior is observed in the global quantity used to characterize the spatiotemporal dynamics.     

On–off intermittency and coherent bursting in stochastically-driven coupled maps

On–off intermittency is a phase space mechanism for bursting in dynamical systems. Here we recall how the simple example of a logistic map with a time-dependent control parameter, considered as a dynamical variable of the system, gives rise to bursting or on–off behavior. We show that, for a given realization of the driver, a stochastically driven logistic map in the on–off intermittent regime always converges to the same temporal dynamics, independently of initial conditions. In that sense, the map is not chaotic. We then explore the behavior of two coupled on–off logistic maps, each driven by a separate random process, and show that, for a wide range of coupling strengths, bursting becomes at least partially coherent. The bursting coherence has a smooth dependence on the coupling parameter and no sharp transition from coherence to incoherence is detected. In the system of two coupled on–off maps studied here, coherent bursting is rooted in the behavior during off phases when the mapped coordinates take on extremely small values.     

Chaotic phenomena on a coupled nonlinear oscillator based on the rollins-hunt's model

Based on the Rollins-Hunt's model, chaotic phenomena in a driven coupled R-L-diode oscillator are examined numerically. It is found that a straightforward extension of this model to a system with two degrees of freedom is valid as far as the quasiperiodic route to chaos is concerned. However, this model is not sufficient to explain the intermittency and the quasiperiodic routes including the discontinuous (jump) bifurcations with hysteresis. Then it is shown that the additional nonlinearity due to variable capacitance of the diode is effective to explain the above phenomena. It is also shown that a two-dimensional discrete return map in which nonlinear terms are introduced in a characteristic form simulates systematically the numerical results. In particular, this map model can explain effectively the mechanisms which cause the intermittency and the cliscontinuous bifurcation.     

Synchronization of systems of Marcus canonical equations driven by α-stable noises

Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties. A coupled dynamical system under non-Gaussian Lévy noise is considered. After discussing cocycle property, stationary orbits and random attractors, a synchronization phenomenon is shown to occur, when the drift terms of the coupled system satisfy certain dissipativity conditions. The synchronization result implies that coupled dynamical systems share a dynamical feature in certain asymptotic sense.     

Explanation of appearance and characteristics of intermittency chaos of the impact oscillator

Chaotic motion of an intermittency type of the impact oscillator appears near segments of saddle-node stability boundaries of subharmonic motions with two different impacts in motion period, which is n multiple (n3) of excitation period. Chaotic motion arises due to an additional impact, which interrupts the process of instability. It is proved and shown by numerical simulations of the system motion. More detail characteristics of the intermittency chaos are evaluated. Described phenomena present a non-usual example, when transition cross special segments of saddle-node stability boundaries of subharmonic impact motions is reversible.     

Fractal systems of central places based on intermittency of space-filling

The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies. However, the underlying rationale of central place fractals in the real world has not yet been revealed so far. This paper is devoted to illustrating the mechanisms by which the fractal patterns can be generated from central place systems. The structural dimension of the traditional central place models is d = 2 indicating no intermittency in the spatial distribution of human settlements. This dimension value is inconsistent with empirical observations. Substituting the complete space filling with the incomplete space filling, we can obtain central place models with fractional dimension D < d = 2 indicative of spatial intermittency. Thus the conventional central place models are converted into fractal central place models. If we further integrate the chance factors into the improved central place fractals, the theory will be able to explain the real patterns of urban places very well. As empirical analyses, the US cities and towns are employed to verify the fractal-based models of central places.     

Control of synchronization and spiking regularity by heterogenous aperiodic high-frequency signal in coupled excitable systems

This paper investigates the synchronization and spiking regularity induced by heterogenous aperiodic (HA) signal in coupled excitable FitzHugh–Nagumo systems. We found new nontrivial effects of couplings and HA signals on the firing regularity and synchronization in coupled excitable systems without a periodic external driving. The phenomenon is similar to array enhanced coherence resonance (AECR), and it is shown that AECR-type behavior is not limited to systems driven by noises. It implies that the HA signal may be beneficial for the brain function, which is similar to the role of noise. Furthermore, it is also found that the mean frequencies, the amplitudes and the heterogeneity of HA stimuli can serve as control parameters in modulating spiking regularity and synchronization in coupled excitable systems. These results may be significant for the control of the synchronized firing of the brain in neural diseases like epilepsy.     

Monte Carlo simulation of boundary layer transition

A statistical method for simulating a boundary layer transition flow is proposed as based on experimental data on the kinematics and dynamics of turbulent spots (Emmons spots) on a flat plate placed in an incompressible fluid. The method determines intermittency with allowance for overlapping spots, which makes it possible to determine the forces on the plate surface and the flow field near the transition region if the mean streamwise velocity field in a developed turbulent boundary layer is known as a function of the Reynolds number. In contrast to multiparameter transition models, this approach avoids the use of nonphysical parameter values.     

Flatness-based control without prediction: example of a vibrating string

Stable trajectory tracking by boundary control is discussed for a string with a mass at its free end. Based on the known fact that the ring of operators used to describe the system is a Bézout ring it is shown that predictions are not required for stabilization if distributed delays are admitted. The method is rather general for systems of boundary coupled wave equations with boundary control that can be modeled as delay systems with commensurate delays. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mode decomposition for a synchronous state and its applications

Synchronization of coupled dynamical systems including periodic and chaotic systems is investigated both anlaytically and numerically. A novel method, mode decomposition, of treating the stability of a synchronous state is proposed based on the Floquet theory. A rigorous criterion is then derived, which can be applied to arbitrary coupled systems. Two typical numerical examples: coupled Van der Pol systems (corresponding to the case of coupled periodic oscillators) and coupled Lorenz systems (corresponding to the case of chaotic systems) are used to demonstrate the theoretical analysis.     

Intermittencies on tori: A way to characterize them

Since the three types of intermittency have been theoretically described, many experimental observations of such regimes have been reported. Chaotic behaviors occurring after torus breakdowns and quasi-periodic regimes are also very often observed. It is not so surprising that intermittencies on tori were never reported as soon as it is understood that these common characteristic of intermittencies should be investigated in a Poincaré section of a Poincaré section, that is, in a set which is not possible to define. A specific approach is therefore required to identify them as shown in the paper with two examples of type-I intermittency on tori solution to two different systems.     

Noise and coupling induced synchronization in a network of chaotic neurons

The synchronization in four forced FitzHugh–Nagumo (FHN) systems is studied, both experimentally and by numerical simulations of a model. We show that synchronization may be achieved either by coupling of systems through bidirectional diffusive interactions, by introducing a common noise to all systems or by combining both ingredients, noise and coupling together. Here we consider white and colored noises, showing that the colored noise is more efficient in synchronizing the systems respect to white noise. Moreover, a small addition of common noise allows the synchronization to occur at smaller values of the coupling strength. When the diffusive coupling in the absence of noise is considered, the system undergoes the transition to subthreshold oscillations, giving a spike suppression regime. We show that noise destroys the appearance of this dynamical regime induced by coupling.     

Micro diffuser flow modeling for cold gas propulsion systems

The use of highly diluted and hypersonic gas flow is in the scope of application of cold gas thrusters for space applications. Satellites and small spacecrafts are navigated to their orbital trajectory with these nozzles. Inside these propulsion systems high density gradients are dominating the efficiency and the thrust steering behavior of the propulsion systems. Micro flows in the transient regime between free molecular flow and continuous flow are not able to be computed with trustworthy results by using a continuous model with no-slip boundary conditions. Therefore boundary slip-velocity models are used for modeling the reduced wall shear stress. Molecular shear stresses decrease the molecular mean velocity near the wall. With a Knudsen number depending slip-velocity model the effective shear stress is computed by the mean gradient of the velocity profile near the wall. In the present study a trans-sonic nozzle flow is computed by using a calibrated velocity slip model what depends on the Knudsen number. The Knudsen numbers are lower the Kn=1 at the nozzle neck of the propulsion system. The results are compared with simulation results of a uniform channel flow and computations of the corresponding no-slip approach. The differences in the hypersonic region are following discussed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Long Nonlinear Water Waves in a Channel Near a Cut-off Frequency

A theoretical study is made of the free-surface flow induced by a wavemaker, performing torsional oscillations about a vertical axis, in a shallow rectangular channel near a cut-off frequency. Exactly at cut-off, linearized water-wave theory predicts a temporally unbounded response due to a resonance phenomenon. It is shown, through a perturbation analysis using characteristic variables, that the nonlinear response is governed by a forced Kadomtsev—Petviashvili (KP) equation with periodic boundary conditions across the channel. This nonlinear initial-boundary-value problem is investigated analytically and numerically. When surface-tension effects are negligible, the nonlinear response reaches a steady state and exhibits jump phenomena. On the other hand, in the high-surface-tension regime, no steady state is obtained. These results are discussed in connection with similar forced wave phenomena studied previously in a deepwater channel and related laboratory experiments.