Periodic Oscillations Research Articles

Dynamics of coupled erbium-doped fiber lasers: Modulation effects and synchronization patterns

Studying the dynamics of coupled Erbium-Doped Fiber Lasers helps in optimizing the performance of these systems in different applications. An important factor in these systems is the modulation signal which can affect the dynamics of systems, leading to complex behaviors including diverse periodic and chaotic dynamics. This paper investigates the dynamics of a ring network of Erbium-Doped Fiber Lasers and compares its behaviors in the presence and absence of the modulation. The results reveal that although complete synchronization is not reachable, certain synchronization patterns exist during the periodic oscillations. In the non-modulated network, two distinct clusters are formed which can achieve lag synchronization under specific coupling intensities. While in the coupled modulated systems, the chimera state may form. These findings represent the complex relationship among modulation, coupling intensity, and network dynamics in EDFL systems.

DYNAMIC ANALYSIS AND HAMILTONIAN ENERGY ASPECTS OF HYPERCHAOTIC MEGASTABLE OSCILLATOR

Megastable oscillations are a subject of significant research interest due to their broad range of potential applications. Typically, megastable systems are driven into oscillation by a forcing term. In this paper, we propose a novel megastable oscillator that utilizes a combination of Signum and trigonometric functions. To the best of our knowledge, no 3D megastable system has been found to exhibit hyperchaotic behavior without any forcing term. We demonstrate the megastability of our oscillator using phase portraits and basins of attraction and confirm the oscillations using the Hamiltonian energy method. We also conduct a stability analysis to explore the system’s nature and investigate the impact of parameters using a bifurcation diagram. Furthermore, we present a Lyapunov spectrum to identify regions of chaos, hyperchaos, and periodic oscillations. The results we obtain demonstrate the complexity of the system and its sensitivity to initial conditions, making it well-suited for applications such as random number generation and secure communication.

Experimental Study on Submerged Nozzle Damping Characteristics of Solid Rocket Motor

Acoustic instabilities in solid rocket motors (SRMs) can lead to severe performance deterioration and structural damage. Nozzle damping accounts for the main acoustic dissipation source, and it is highly dependent on geometric parameters and operating conditions. This study experimentally investigated the acoustic damping characteristics of submerged nozzles in SRMs, focusing on the effects of submerged cavity dimensions, nozzle convergent angle, throat-to-port area ratio, and mean pressure variations on the longitudinal instability. The steady-state wave decay method was used to quantify the acoustic damping, and a designed rotary valve system was employed to introduce periodic pressure oscillations in the high-pressure combustion chamber. The results revealed that a larger submerged cavity would reduce the nozzle damping efficiency, with the elimination of the submerged cavity enhancing the nozzle decay coefficient magnitude by 41.9%. Furthermore, increasing the nozzle convergent angle was found to amplify acoustic wave reflection, thereby diminishing damping performance. A linear inverse relationship was observed between the throat-to-port area ratio and the decay coefficient, with a 125% increase in the ratio resulting in a 24.3% reduction in the decay coefficient. Interestingly, despite the formation of complex vortices in the submerged cavity, the mean pressure variation presented negligible effects on acoustic damping characteristics, and its damping performance is similar to a simple nozzle without a cavity. These findings provide valuable experimental data for predicting the stability of a solid rocket motor with a submerged nozzle and offer insights into the optimization of submerged nozzle designs for higher acoustic damping in SRMs.

Stability and Hopf Bifurcation Analysis of a Predator–Prey Model with Weak Allee Effect Delay and Competition Delay

The purpose of this paper is to study a predator–prey model with Allee effect and double time delays. This research examines the dynamics of the model, with a focus on positivity, existence, stability and Hopf bifurcations. The stability of the periodic solution and the direction of the Hopf bifurcation are elucidated by applying the normal form theory and the center manifold theorem. To validate the correctness of the theoretical analysis, numerical simulations were conducted. The results suggest that a weak Allee effect delay can promote stability within the model, transitioning it from instability to stability. Nevertheless, the competition delay induces periodic oscillations and chaotic dynamics, ultimately resulting in the population’s collapse.

Preferential enhancement of convective heat transfer over drag via near-wall turbulence manipulation using spanwise wall oscillations

This study investigates the manipulation of convective heat transfer through spanwise wall oscillations in a turbulent channel flow. Direct numerical simulations are performed at Reτ=180 and Pr=1.The primary focus of this work is to explore the heat transfer response to oscillation parameters that promote drag increase, a regime that has received limited attention. By adopting an extended oscillation period (T+=500) and amplitude (W+=30), which have been reported to enhance drag, a remarkable dissimilarity between momentum and heat transport emerges. Under these conditions, the convective heat transfer undergoes a substantial 15% intensification, while the drag increases by a comparatively moderate 7.7%, effectively breaking the Reynolds analogy. To elucidate the physical mechanisms responsible for this dissimilar behaviour, a comprehensive statistical analysis is conducted. The control effect on the near-wall streaks and the associated mixing of momentum and heat is investigated by examining the energy distribution across scales and wall-normal locations. This analysis provides valuable insights into the control’s impact on the turbulent structures. Furthermore, the correlation between wall-normal velocity fluctuations and both streamwise velocity and temperature fluctuations is scrutinized to understand the modification of sweep and ejection events, which drive the transport of momentum and heat. The Fukagata–Iwamoto–Kasagi (FIK) identity is employed to identify the contributing factors to the changes in drag and heat transfer. The analysis highlights the importance of the pressure term in the streamwise velocity equation and the linearity of the temperature equation. Further investigation is necessary to fully unravel the complex mechanisms governing the decoupling of heat and momentum transport. The results of this study underscore the potential of using unconventional spanwise wall oscillations parameters to preferentially enhance convective heat transfer while minimizing the associated drag penalty.

Aperiodic Component Analysis in Quantification of Steady-State Visually Evoked Potentials.

In this study, we aimed to investigate whether and how the aperiodic component in electroencephalograms affects different quantitative processes of steady-state visually evoked potentials and the performance of corresponding brain-computer interfaces. We applied the Fitting Oscillations & One-Over-F method to parameterize power spectra as a combination of periodic oscillations and an aperiodic component. Electroencephalographic responses and system performance were measured and compared using four prevailing methods: power spectral density analysis, canonical correlation analysis, filter bank canonical correlation analysis and the state-of-the-art method, task discriminant component analysis. We found that controlling for the aperiodic component prominently downgraded the performance of brain-computer interfaces measured by canonical correlation analysis (94.9% to 82.8%), filter bank canonical correlation analysis (94.1% to 87.6%), and task discriminant component analysis (96.5% to 70.3%). However, it had almost no effect on that measured by power spectral density analysis (80.4% to 78.7%). This was accompanied by a differential aperiodic impact between power spectral density analysis and the other three methods on the differentiation of the target and non-target stimuli. The aperiodic component distinctly impacts the quantification of steady-state visually evoked potentials and the performance of corresponding brain-computer interfaces. Our work underscores the significance of taking into account the dynamic nature of aperiodic activities in research related to the quantification of steady-state visually evoked potentials. The source code for our approach is available at https://github.com/didi226/scut_ssvep_aperiod.

Attracting dynamical modes of highly elastic fibres settling under gravity in a viscous fluid

The dynamics of a single highly elastic fibre settling under gravity in a very viscous fluid is studied numerically. We employ the bead model and multipole expansion of the Stokes equations, corrected for lubrication that is implemented in the precise Hydromultipole numerical codes. Four attracting regular dynamical modes of highly elastic fibres are found: two stationary shapes (one translating and the other rotating and translating), and two periodic oscillations around such shapes. The phase diagram of these modes is presented. It illustrates that the existence of each mode depends not only on the elasto-gravitation number but also on the fibre aspect ratio. Characteristic time scales, fibre deformation patterns and motion in the different modes are determined.

Investigation of block interleavers in OFDM radio communication systems with convolutional encoding in multipath channels with fast fading

Noise immunity codecs are good at correcting single errors. Group errors often occur in multipath radio channels with fading. Interleaving is used to convert group errors into single errors. Matching the interleaver structure with the signal and code parameters allows the interleaver to work efficiently. Optimization of the interleaver parameters depending on the characteristics of the communication channel increases the efficiency of the interleaver. The purpose of the work is to determine the parameters of block interleavers for an OFDM radio communication system with convolutional coding in conditions of signal scattering in time and frequency. A model of a channel with two beams and Rayleigh fades is considered. The influence of interleaver parameters on the noise immunity of the OFDM radio communication system depending on the channel parameters (fading rate, multipath interval) has been analyzed. Block deterministic and pseudorandom interleavers are considered. With magnification lengths the interleaver increases noise immunity of the communication system. But at the same time, the delay in transmitting the message increases. The optimal length has been determined, providing a compromise between delay and noise immunity. This length is determined depending on the coherence time of the channel. The number of rows of the matrix interleaver is depending on the decoding depth. This is the number of rows provides better noise immunity at optimal length. But sometimes the optimal length is too long. Therefore a function has been introduced that characterizes the minimum distance between bits in the “time-frequency-code” space at the input of the interleaver. The distance between the bits in the time domain is normalized for the coherence time of the channel. The distance between the bits in the frequency domain is calculated as a normalized deviation from the oscillation period in the signal power spectrum at the output of a channel with two beams. The distance between the bits in the “code space” is calculated as the distance normalized the effective decoding depth of the code used. Given the function describes optimal and critical values well parameters of deterministic interleavers of any length. Deterministic interleavers have a higher probability of error per bit than random interleavers. The definition of parameters using the proposed function allows the deterministic interleaver to work with the same low the probability of error per bit as well as random interleavers.

Glucokinase activity controls subpopulations of β-cells that alternately lead islet Ca2+ oscillations.

Oscillations in insulin secretion, driven by islet Ca2+ waves, are crucial for glycemic control. Prior studies, performed with single-plane imaging, suggest that subpopulations of electrically coupled β-cells have privileged roles in leading and coordinating the propagation of Ca2+ waves. Here, we used 3D light-sheet imaging to analyze the location and Ca2+ activity of single β-cells within the entire islet at >2 Hz. In contrast with single-plane studies, 3D network analysis indicates that the most highly synchronized β-cells are located at the islet center, and remain regionally but not cellularly stable between oscillations. This subpopulation, which includes 'hub cells', is insensitive to changes in fuel metabolism induced by glucokinase and pyruvate kinase activation. β-cells that initiate the Ca2+ wave ('leaders') are located at the islet periphery, and strikingly, change their identity over time via rotations in the wave axis. Glucokinase activation, which increased oscillation period, reinforced leader cells and stabilized the wave axis. Pyruvate kinase activation, despite increasing oscillation frequency, had no effect on leader cells, indicating the wave origin is patterned by fuel input. These findings emphasize the stochastic nature of the β-cell subpopulations that control Ca2+ oscillations and identify a role for glucokinase in spatially patterning 'leader' β-cells.

The role of dynamic friction in the appearance of periodic oscillations in mechanical systems

This article investigates the appearance of periodic mechanical oscillations associated with the transition between static and dynamic friction regimes. The study employs a mechanical system with one degree of freedom and a friction model recently proposed by Brown and McPhee, whose continuity and differentiability properties make it particularly appropriate for an analytical treatment of the equations. A bifurcation study of the system, including stability analysis, transformation to normal form and numerical continuation techniques, reveals that stable periodic orbits can be created either by a supercritical Hopf bifurcation or by a saddle-node bifurcation of limit cycles. The influence of all system parameters on the appearance of periodic oscillations is investigated in detail. In particular, the effect of the friction model parameters (static-to-dynamic friction ratio and transition speed between the static and dynamic regimes) on the bifurcation behavior of the system is addressed.

Thermo-optical tweezers based on photothermal waveguides

Field-controlled micromanipulation represents a pivotal technique for handling microparticles, yet conventional methods often risk physical damage to targets. Here, we discovered a completely new mechanism for true noncontact manipulation through photothermal effects, called thermal-optical tweezers. We employ a laser self-assembly photothermal waveguide (PTW) for dynamic microparticle manipulation. This waveguide demonstrates superior photothermal conversion and precision control, generating a nonisothermal temperature field. The interaction of thermal convection and thermophoresis within this field creates a microfluidic potential well, enabling noncontact and nondestructive particle manipulation. By varying the path of PTWs in lithography and manipulating laser loading modes, diverse manipulation strategies, such as Z-shaped migration, periodic oscillation, and directional transport, are achievable. Our innovative noninvasive micromanipulation technology minimizes not only physical damage to target objects but also enables precise and diverse manipulation of micro entities, opening up new avenues for the photothermal control of cells and biomolecules.

Computational modeling establishes mechanotransduction as a potent modulator of the mammalian circadian clock.

Mechanotransduction, which is the integration of mechanical signals from the external environment of a cell to changes in intracellular signaling, governs many cellular functions. Recent studies have shown that the mechanical state of the cell is also coupled to the cellular circadian clock. To investigate possible interactions between circadian rhythms and cellular mechanotransduction, we have developed a computational model that integrates the two pathways. We postulated that translocation of the transcriptional regulators MRTF (herein referring to both MRTF-A and MRTF-B), YAP and TAZ (also known as YAP1 and WWTR1, respectively; collectively denoted YAP/TAZ) into the nucleus leads to altered expression of circadian proteins. Simulations from our model predict that lower levels of cytoskeletal activity are associated with longer circadian oscillation periods and higher oscillation amplitudes, which is consistent with recent experimental observations. Furthermore, accumulation of YAP/TAZ and MRTF in the nucleus causes circadian oscillations to decay in our model. These effects hold both at the single-cell level and within a population-level framework. Finally, we investigated the effects of mutations in YAP or lamin A, the latter of which result in a class of diseases known as laminopathies. In silico, oscillations in circadian proteins are substantially weaker in populations of cells with mutations in YAP or lamin A, suggesting that defects in mechanotransduction can disrupt the circadian clock in certain disease states; however, reducing substrate stiffness in the model restores normal oscillatory behavior, suggesting a possible compensatory mechanism. Thus, our study identifies that mechanotransduction could be a potent modulatory cue for cellular clocks and that this crosstalk can be leveraged to rescue the circadian clock in disease states.

Solar Atmospheric Oscillations as Measured by the GOES-R Series EXIS EUVS-C Instrument

This Letter presents first observations of distinct solar atmospheric oscillations from signals collected by the Extreme Ultraviolet and X-ray Irradiance Sensors EUVS-C instrument, which is part of each Geostationary Observational Environmental Satellite R-Series instrument payload. The EUVS-C instrument is a full-disk, normal-incidence spectrograph that covers a narrow band in the mid-ultraviolet between 276 and 284 nm, where it can measure the magnesium ii emission doublet at ∼280 nm and the photospheric continuum. The primary goal of EUVS-C data is to construct the well-known Mg ii index, which is often used as a proxy for chromospheric activity. Because of the high temporal and spectral resolution of EUVS-C measurements, the data provide a unique opportunity to observe discernible solar atmospheric waves that have definite signatures of 3 and 5 minute oscillation periods, where the frequency response of these signals is dependent on what part of the spectrum is analyzed (e.g., Mg emission lines). Furthermore, both photospheric and chromospheric waves can simultaneously be examined. With the recent increase in solar activity for Solar Cycle 25, these waves exhibit enhanced amplitudes and phase shifts during the impulsive shock of strong solar flares. This Letter will discuss the analysis for deriving these waves, and results from both a quiescent Sun and an X-class solar flare event will be presented.

Oscillatory one-roll and two-roll solutions in laminar viscoelastic Rayleigh-Bénard convection in a square cavity

Rayleigh-Bénard convection in square closed cavities filled with Oldroyd-B fluid was studied using OpenFOAM-based RheoTool. For the RBC in Newtonian fluids, the transition always occurs from conduction to steady state convection with increasing Rayleigh number (Ra). On the other hand, the viscoelastic fluids may also show the transition from conduction to oscillatory convection. Further increase in Ra may result in a steady state convective solutions. It is further noted that the behavior is similar to Newtonian fluids for larger values of viscosity ratio (B). Considering the abovementioned different flow behavior at different values of the parameters, it is noted that there are five different types of solutions possible for the viscoelastic fluids viz. pure conduction (PC), one roll periodic oscillations (ORPO), one roll steady state (ORSS) convection, two roll periodic oscillations (TRPO), simultaneous one and two roll steady state convection. Therefore, a bifurcation diagram in the parametric space of Ra and B is presented, depicting these five regions corresponding to each type of solution. The boundaries of these regions have been identified by numerical simulation. Note that all these regions exist in the laminar flow regime, and the transition to turbulence is not considered here. Interestingly, at low values of B, as one increases Ra, it is seen that the ORSS region is sandwiched between ORPO and TRPO. The likely reason for this interesting behavior is explained. Moreover, representative solutions in each region in terms of isotherms, streamlines, and vector plots have been included to demonstrate the dynamics of each delineated region.

Understanding the heat release fluctuations and combustion noise characteristics of non-premixed co/counter-swirl syngas flames at MILD conditions

The heat release fluctuations and combustion noise of co/counter-swirl non-premixed syngas (mixture of CO and H2) and air flames at moderate or intense low-oxygen dilution (MILD) conditions has been investigated experimentally using simultaneous OH∗-chemiluminescence (5 kHz) and microphone measurements (50 kHz). Furthermore, the similarities and differences between co and counter-swirl flames are elucidated using proper orthogonal decomposition (POD), spectrogram, and frequency distributions. At a high O2 concentration (21% by volume), noise measurements for both co/counter-swirl flames comprise both high-amplitude periodic and low-amplitude aperiodic oscillations, revealing signatures of intermittency. Interestingly, for periodic oscillations, the global luminosity (Ifluc) obtained from OH∗-chemiluminescence and noise (Pfluc) are found to be in phase, indicating a strong coupling between noise and heat-release rate. Moreover, POD modes indicate that the global heat release fluctuation occurring in the central region of the combustor is the source of these periodic fluctuations. Besides global fluctuation, the heat release region undergoes rotation around the combustor axis with differing frequencies for co and counter-swirl flames. Furthermore, the global fluctuation is found to be prominent for co-swirl flames, while precession motion is more pronounced in counter-swirl flames. When O2 is reduced to 13.13%, the combustion becomes stable, as suggested by low-amplitude aperiodic oscillations in the noise measurement. Heat release of co and counter-swirl flames respond differently to this reduction in O2 concentration. The precession motion remains unaffected for co-swirl flames upon O2 reduction. In contrast, precession motion alters significantly for counter-swirl. Regarding global fluctuations, low oxygen concentration suppresses all periodic fluctuations, mitigates noise, and Pfluc and Ifluc become entirely decoupled for both flames. Hence, the present study demonstrates for the first time the applicability of a low-oxygen dilution strategy in the context of co/counter-swirl flames for decoupling heat release and noise measurements. Furthermore, the study also indicates the varied response of complex co and counter-swirl flames to different oxygen concentrations.

Research on the flame oscillation characteristics of scramjet combustor equipped with strut fuel injector

The combustor is the core component of the scramjet engine, and stable combustion is the prerequisite for the efficient operation of the scramjet engine. This paper investigates combustion stability in a combustor with a thin strut for oxygen supplementation at the trailing edge. LES (Large eddy simulation) was carried out under the combustor inlet conditions of Ma= 2.8, Tt= 1680 K, and Pt= 1.87 MPa. The results show that as the amount of oxygen supplementation inside the combustor increases, the oscillation forward propagation characteristics of the flame front inside the combustor are formed. First, the combustion instability phenomenon of the flame inside the combustor is analyzed, and then the oscillation frequency of the flame is analyzed by FFT (Fast Fourier Transform) of the flame front and pressure and DMD (Dynamic Mode Decomposition) of the velocity field within one cycle. Finally, the flame forward propagation mechanism inside the combustor is analyzed by pressure-velocity-heat release distribution. The results show that the injection of excess oxygen inside the combustor forms a strong coupling phenomenon of flow and combustion, and the premixed gas downstream of the trailing edge of the strut forms a state of slow combustion to explosion, forming a flame propagation forward and periodic oscillation phenomenon.

Diversity, Stability, and the Forecast Challenge in Forest Lepidopteran Predictive Ecology: Are Multi-Scale Plant–Insect Interactions the Key to Increased Forecast Precision?

I report on long-term patterns of outbreak cycling in four study systems across Canada and illustrate how forecasting in these systems is highly imprecise because of complexity in the cycling and a lack of spatial synchrony amongst sample locations. I describe how a range of bottom-up effects could be generating complexity in these otherwise periodic systems. (1) The spruce budworm in Québec exhibits aperiodic and asynchronous behavior at fast time-scales, and a slow modulation of cycle peak intensity that varies regionally. (2) The forest tent caterpillar across Canada exhibits eruptive spiking behavior that is aperiodic locally, and asynchronous amongst regions, yet aggregates to produce a pattern of periodic outbreaks. In Québec, forest tent caterpillar cycles differ in the aspen-dominated northwest versus the maple-dominated southeast, with opposing patterns of cycle intensity between the two regions. (3) In Alberta, forest tent caterpillar outbreak cycles resist synchronization across a forest landscape gradient, even at very fine spatial scales, resulting in a complex pattern of cycling that defies simple forecasting techniques. (4) In the Border Lakes region of Ontario and Minnesota, where the two insect species coexist in a mixedwood landscape of hardwood and conifers, outbreak cycle intensity in each species varies spatially and temporally in response to host forest landscape structure. Much attention has been given to the effect of top-down agents in driving synchronizable population cycles. However, foliage loss, tree death, and forest succession at stem, stand, and landscape scales affect larval and adult dispersal success, and may serve to override regulatory processes that cause otherwise top-down-driven periodic, synchronized, and predictable population oscillations to become aperiodic, asynchronous, and unpredictable. Incorporating bottom-up effects at multiple spatial and temporal scales may be the key to making significant improvements in forest insect outbreak forecasting.

Deformation of Sessile Droplets under a Gentle Shear Airflow.

Deformation of sessile droplets under shear flow is widespread in both nature and industry. Previous research focuses on the shedding process of sessile droplets under shear airflow, with insufficient attention paid to the droplet deformation before shedding. In this work, experimental studies on the deformation behaviors of sessile droplets under shear airflow are conducted to investigate the effects of airflow velocity and droplet volume on the tangential and normal droplet deformations. Scaling laws of the droplet deformations are established. The results show that the profile of sessile droplets changes under shear airflow with the topmost point exhibiting periodic oscillations in both tangential and normal directions. The oscillation period of the tangential deformation exceeds that of the normal deformation. The average tangential deformation of droplets increases with the increasing airflow velocity and droplet volume. The average normal deformation of droplets increases with the increasing airflow velocity and is influenced by the droplet volume at a higher airflow velocity. The contact angle on the windward side oscillates periodically, and its average value significantly decreases. The contact angle of droplets on the windward side decreases as the airflow velocity and droplet volume increase, while the contact angle on the leeward side remains almost unchanged. The average deformation of droplets in the tangential and normal directions is linearly related to the effective Weber number and the square of the effective Weber number. These findings could be used to predict the deformation of sessile droplets under shear airflows.

Revealing Hidden Features of Chaotic Systems Using High-Performance Bifurcation Analysis Tools Based on CUDA Technology

Bifurcation analysis is an essential tool in nonlinear dynamics. Bifurcation diagrams help to discover subtle features of investigated dynamics such as chaotic and periodic regimes, hidden attractors and fixed points. However, plotting high-resolution bifurcation diagrams can be a computationally challenging task, especially in multiparametric evaluation. It should be noted that the bifurcation analysis is a task with natural parallelism and thus can be efficiently solved using hybrid central-graphics processing architectures. In this paper, we propose an advanced algorithm and special software for plotting bifurcation diagrams using calculations accelerated by graphics processing unit in combination with a highly efficient semi-implicit ordinary differential equation solver. Time series processing is based on the extraction of amplitude and phase features for the density-based spatial clustering of applications with noise to determine oscillation periodicity. We showcase the features of the application of proposed solutions on a set of test chaotic systems. The performance of the analysis algorithms is investigated in comparison with conventional solutions based on central processing unit and several approaches known from the literature. We explicitly show that the proposed algorithm outperforms known solutions in both calculation speed and precision.

Intermittent microwave bursts of a semiconductor laser with an ultra-long loop for generating timing-based random bits.

Chaotic dynamics of semiconductor lasers under optical feedback are useful for random bit generation (RBG). By exploring on an ultra-long feedback loop, a single-mode laser in a route-to-chaos unveils an emission intensity with intermittent microwave bursts, for which a fast form of timing-based RBG is demonstrated. Each microwave burst corresponds to a packet of periodic intensity oscillations at the relaxation resonance. Numerous bursts are found intermittently within a round trip. Repetitions of these intermittent microwave bursts are observed across consecutive round trips. Randomness is extracted from the timing of the bursts as far as the feedback is reinitialized. With a 5-km fiber for feedback to the laser, over 104 intermittent bursts of microwave at 7 GHz are obtained per round trip, where the irregular timing in the envelope leads to RBG at 9.6 Gbps. Such experimental results feature the form of timing-based RBG that is very fast by comparison, carried by the microwave, and stored in the feedback nonlinear dynamics.