Period-doubled States Research Articles

Numerical study on mechanisms of period-doubling bifurcation in pulsed dielectric barrier discharges at atmospheric pressure

In this paper, the mechanisms of the period-doubling bifurcation in pulsed Dielectric Barrier Discharges (DBDs) are numerically investigated at atmospheric pressure. Under the given discharge conditions, the pulsed DBDs could maintain a normal period-1 (P1) state at relatively larger repetition frequencies over 40 kHz, by decreasing the repetition frequency, namely, keeping the duration of the power-on phase unchanged but increasing the duration of the power-off phase, the simulation shows that the discharge bifurcates into a period-2 (P2) state after a transient period of instability. Although the charged particles can diffuse to the surface of dielectric plates more fully at a lower repetition frequency, the large quantities of ions in the sheath region produced by the relatively larger discharge current that have not yet dissipated completely before the next discharge event are proposed to play an important role in the discharge bifurcation process, and the spatial profiles of the charged particle density, electric field, and space charge density in the sheath region before the discharge ignition are examined deeply to further explore the corresponding underpinning physics. The large density of residual ions in the sheath region with the enhanced electric field can weaken the subsequent discharge event and induce the discharge to enter the period-doubling state. Moreover, the computational data indicate that the discharge evolves into the period-4 (P4) and period-8 (P8) state when the repetition frequency approaches 30 and 26 kHz at the given discharge conditions. The simulation data can effectively facilitate the understanding of the temporal nonlinear behaviors in pulsed DBDs and propose ways to further control the plasma stability in applications.

Self-pulsing and chaos in the asymmetrically driven dissipative photonic Bose-Hubbard dimer: A bifurcation analysis.

We perform a systematic study of the temporal dynamics emerging in the asymmetrically driven dissipative Bose-Hubbard dimer model. This model successfully describes the nonlinear dynamics of photonic diatomic molecules in linearly coupled Kerr resonators coherently excited by a single laser beam. Such temporal dynamics may include self-pulsing oscillations, period doubled oscillatory states, chaotic dynamics, and spikes. We have thoroughly characterized such dynamical states, their origin, and their regions of stability by applying bifurcation analysis and dynamical system theory. This approach has allowed us to identify and classify the instabilities, which are responsible for the appearance of different types of temporal dynamics.

Hysteresis of two-dimensional flows around a NACA0012 airfoil at [formula omitted] and linear analyses of their mean flow.

Two-dimensional numerical simulations of the flow around a NACA0012 profile at Reynolds number Re=5000 show that unsteady periodic flows reach different saturated states when increasing or decreasing the angle of attack between 7∘ and 8∘. Within this range, the lift signal shows co-existing periodic states and period-doubling, as the wake undergoes a substantial change in character from the standard von-Kármán vortex street. Results of experiments in a water channel also indicate a change of the flow topology but at slightly lower angles of attack α=6°. A discussion of the discrepancy between numerical and experimental results is proposed in light of results about the three-dimensional transition of wake flows behind bluff bodies and airfoils. Finally, eigenvalue and resolvent analyses of time-averaged flows are used to investigate the two-dimensional transitions further. While a peak of energetic amplification is obtained at the frequency of a single periodic state, a double peak is observed for co-existing periodic states, the second one being at the frequency of the periodic state not used to compute the time-averaged flow. This behaviour also characterizes the resolvent analysis of the period-doubled states, although less pronounced.

Bifurcation and chaos behaviors of Lyapunov function controlled PWM boost converter

In this paper, we have derived the mathematical model of the Lyapunov function-based boost converter, which is essentially a voltage and current double-loop controller, and studied the stability of the closed-loop modulation system. The analysis shows that the Lyapunov function controlled boost converter is not globally asymptotically stable when the switching frequency is limited. We also used a Monodromy matrix to analyze the nonlinear dynamic behavior of the system. It is found that with the decrease of the reference current, the Monodromy matrix eigen multiplier gradually jumps from inside to the outside on the unit circle, and correspondingly, the converter will move from the period-one steady state to period-doubling state, and then period-doubling state to the chaotic state. Simulation and experimental results show that the theoretical analysis is correct.

Dynamics Analysis of Rolling Bearings for Motor of a Mobile Power Station

The electric motor is an important part of a mobile power station. Under the complex operating conditions, the stiffness of the rolling bearing exhibits strong time-varying characteristics and non-linear characteristics, which is the one of the main sources for the system non-linearity. Taking the angular contact bearing as the research object, the coupled dynamic model of the bearing-rotor system is established to calculate the time-varying stiffness. The bifurcation law exhibited by the system can be attributed to the excitation of the non-linear bearing force. The numerical calculation method is used to study the motion state bifurcation law and dynamic frequency response characteristics under the rated working condition of the motor. Considering bearing damping, clearance and radial load, the bifurcation and time domain diagrams of different parameters, displacements and rotation speeds in different directions are studied respectively. The results show that when the parameters change, the system will experience chaos, quasi-period and period-doubling motion state; Damping suppresses vibration very clearly, while changes in bearing clearance and radial load significantly cause the system’s vibration amplitude to increase, and radial load changes accelerate system vibration. A reasonable bearing is of great significance for motor the design of a mobile power station.

Breach and recurrence of dissipative soliton resonance during period-doubling evolution in a fiber laser

We report on the experimental observation of period-doubling bifurcation of dissipative-soliton-resonance (DSR) pulses in a fiber laser passively mode-locked by using the nonlinear optical loop mirror. Increasing the pump power of the fiber laser, we show that temporally a stable, uniform DSR pulse train could be transformed into a period-doubling state, exhibiting two sets of pulse parameters between the adjacent cavity roundtrip. It is found that DSR pulses in the period-doubling state could maintain the typical feature of DSR pulse: fixed pulse peak power and linear variation in pulse width with respect to the pump power change. The mechanism for achieving period-doubling of DSR pulses is discussed.

Period Doubling of Dissipative-Soliton-Resonance Pulses in Passively Mode-Locked Fiber Lasers

Period-doubled dissipative-soliton-resonance (DSR) pulses are numerically investigated in a Yb-doped fiber laser based on nonlinear amplifying loop mirror (NALM). In the case of low pump power, stationary dissipative solitons with uniform pulse peak power are obtained in the laser. Further increasing the pump power, the laser operates in the DSR regime, where the phenomenon of period-doubling bifurcations could occur. In a period-doubled state, the pulse peak power returns back to its original one every two cavity roundtrips while the pulse duration remains almost the same. We analyze the effects of cavity parameters on the DSR-pulse features under the dynamic bifurcations. It is found that the saturation power of NALM plays a dominant role in the formation of period-doubled DSR pulses. Our simulation results are conducive to enriching the dynamics of DSR pulses in nonlinear systems.

Detection and parameter estimation of weak pulse signal based on strongly coupled Duffing oscillators

Pulse signal detection is widely used in nuclear explosion electromagnetic pulse detection, lightning signal detection, power system partial discharge detection, electrostatic discharge detection, and other fields. The signal strength becomes weak with the increase of the detection distance and may be submerged in strong Gaussian noise for remote detection. Therefore, the detection and recovery of the weak signals, especially the weak pulse signals, have important applications in signal processing area. Some methods have been reported to detect and estimate weak pulse signals in strong background noise. Coupled Duffing oscillators are usually used in processing periodic signals, though it is still in an exploration stage for aperiodic transient signals. There remain some problems to be solved, for example, the system performance depends on some initial values, results are valid only for the period-doubling bifurcation state, the waveform time domain information cannot be accurately estimated, etc. In this paper, we explain the reasons why there exist these inherent defects in the current weakly coupled Duffing oscillators. In order to solve the above-mentioned problems, a new signal detection and recovery model is constructed, which is characterized by coupling the restoring force and damping force of the two oscillators simultaneously. A large coupling coefficient is applied to the two Duffing oscillators, and a generalized " in-well out-of-synchronization”phenomenon arises between the oscillators which conduces to detecting and recovering the weak pulse signals, and also overcoming the defects mentioned above. Using the metrics of signal-to-noise ratio improvement (SNRI) and waveform similarity, the effects of amplitude and period of periodic driving force, coupling coefficient, step size and damping coefficient on signal detection and waveform recovery are studied. Finally, experiments are performed to detect and recover the following three kinds of pulses: square wave pulses, double exponential pulses, and Gaussian derivative pulses. The input SNR thresholds of these three waveforms are –15, –12, and –16 dB, respectively, under the detection probabilities and waveform similarity all being greater than 0.9 simultaneously. The maximum error of the pulse amplitude and pulse width are both less than 5% of their corresponding true values. In summary, the strongly coupled Duffing system has advantages of being able to operate in any phase-space state and being no longer limited by the initial values. Especially, the time domain waveform of weak pulse signals can be well recovered in the low SNR case, and the error and the minimum mean square error are both very low.

Period-Doubled Bloch States in a Bose–Einstein Condensate**Supported by the National Key Research and Development Program of China under Grant Nos 2016YFA0301501 and 2017YFA0303302, and the National Natural Science Foundation of China under Grants Nos 11334001, 61727819, 61475007 and 91736208.

We study systematically the period-doubled Bloch states for a weakly interacting Bose–Einstein condensate in a one-dimensional optical lattice. This kind of state is of form ψk = eikx ϕk(x), where ϕk(x) is of a period twice the optical lattice constant. Our numerical results show how these nonlinear period-doubled states grow out of linear period-doubled states at a quarter away from the Brillouin zone center as the repulsive interatomic interaction increases. This is corroborated by our analytical results. We find that all nonlinear period-doubled Bloch states have both Landau instability and dynamical instability.

Settling behavior of two particles with different densities in a vertical channel

Sedimentation of two particles with different densities in a two-dimensional channel is studied using the lattice Boltzmann method. We focus on the steady state and periodic state of the settling behavior of the particles, which strongly depend on the Reynolds number Re as well as the density difference α. We show that the particles always reach a steady state if α is small enough at a large Re, while they are predicted to oscillate at a small Re. The staggered configurations in steady state for a wide range of Re and α are presented. Our results also demonstrate that the periodic state of the particles at a small Re is different from that at large Re. One significant difference is that the amplitude of oscillation decreases as α increases when Re is small, while the opposite is true when Re is large. In addition, there exists a narrow range of Re within which we can observe both of the above-mentioned periodic states. At large Re, the effect of α on the periodic motion of particles is quite significant. The phase diagram, constructed using the lateral displacements of the two particles, shows a transition to a period-doubled state on increasing α when Re is large.

Emulating Solid-State Physics with a Hybrid System of Ultracold Ions and Atoms

We propose and theoretically investigate a hybrid system composed of a crystal of trapped ions coupled to a cloud of ultracold fermions. The ions form a periodic lattice and induce a band structure in the atoms. This system combines the advantages of high fidelity operations and detection offered by trapped ion systems with ultracold atomic systems. It also features close analogies to natural solid-state systems, as the atomic degrees of freedom couple to phonons of the ion lattice, thereby emulating a solid-state system. Starting from the microscopic many-body Hamiltonian, we derive the low energy Hamiltonian, including the atomic band structure, and give an expression for the atom-phonon coupling. We discuss possible experimental implementations such as a Peierls-like transition into a period-doubled dimerized state.

The Characteristic Parameter Estimation of Low Temperature Target Weak Signal Based on VanderPol-Duffing System

The weak signal, which is usually submerged in strong noise, is very difficult to detecte for its amplitude and frequency. The dynamic properties of VanderPol-Duffing are studied in this paper. Such system can go into the chaos under certain parameters. In chaotic state the disturbance of weak periodic signals can make the system dynamic behavior change dramatically. Our research results show that the system is from period doubling state to chaotic state when the amplitude of input signal is changed. And it has a remarkable impact influence on the system dynamic performance when the input frequency is varied. The unknown frequency can be detected through counting the numbers of turning point in phase diagram. The simulation results verified that the presented method is feasible and there are a lot of theory values in the research.

Self-organized reactivity patterns during the oxidation of H2–CO mixtures on a rotating Pt ring-electrode

We report the spontaneous formation of spatial reactivity patterns during the oxidation of H2/CO mixtures in diluted perchloric acid on a rotating Pt ring-electrode. Under potentiostatic conditions, the system is oscillatory. At the onset of oscillations at low applied voltage, regular spatio-temporal structures form. At intermediate and high applied voltages spatio-temporal chaos is observed, which exhibits an increasing number of high reactivity spikes with increasing voltage. The transition between the regular and chaotic regime is rather complex and involves period-doubled states. Under galvanostatic conditions, a similar spatio-temporal scenario is observed as a function of applied current.

The transition mechanism from a symmetric single period discharge to a period-doubling discharge in atmospheric helium dielectric-barrier discharge

Period-doubling and chaos phenomenon have been frequently observed in atmospheric-pressure dielectric-barrier discharges. However, how a normal single period discharge bifurcates into period-doubling state is still unclear. In this paper, by changing the driving frequency, we study numerically the transition mechanisms from a normal single period discharge to a period-doubling state using a one-dimensional self-consistent fluid model. The results show that before a discharge bifurcates into a period-doubling state, it first deviates from its normal operation and transforms into an asymmetric single period discharge mode. Then the weaker discharge in this asymmetric discharge will be enhanced gradually with increasing of the frequency until it makes the subsequent discharge weaken and results in the discharge entering a period-doubling state. In the whole transition process, the spatial distribution of the charged particle density and the electric field plays a definitive role. The conclusions are further confirmed by changing the gap width and the amplitude of the applied voltage.

A numerical study of an inline oscillating cylinder in a free stream

AbstractSimulations of a cylinder undergoing externally controlled sinusoidal oscillations in the free stream direction have been performed. The frequency of oscillation was kept equal to the vortex shedding frequency from a fixed cylinder, while the amplitude of oscillation was varied, and the response of the flow measured. With varying amplitude, a rich series of dynamic responses was recorded. With increasing amplitude, these states included wakes similar to the Kármán vortex street, quasiperiodic oscillations interleaved with regions of synchronized periodicity (periodic on multiple oscillation cycles), a period-doubled state and chaotic oscillations. It is hypothesized that, for low to moderate amplitudes, the wake dynamics are controlled by vortex shedding at a global frequency, modified by the oscillation. This vortex shedding is frequency modulated by the driven oscillation and amplitude modulated by vortex interaction. Data are presented to support this hypothesis.

Abrupt change of synchronization of ring coupled Duffing oscillator

The ring coupled Duffing oscillator was investigated, a phenomenon was observed when analyzing the synchronization evolution between coupled oscillators, which shows that if all oscillators are driven by the same periodic driving force,the motion trajectory between weakly coupled oscillators will generate two abrupt changes from synchronization to non-synchronization and then to synchronization in the phase transition of period-doubling bifurcation, chaotic state and large-scale periodic state. Any synchronous abrupt change can be used to rapidly identify system phase transition, and thus a weak periodic signal detection method was proposed based on the phase transition of period-doubling bifurcation and chaotic state.

Control of chaos in an injection multi-quantum well laser via shifting or modulating the injection light

Three methods which can control the chaos in an injection multi-quantum-well (MQW) laser via adjusting or modulating the injection light are presented. Firstly, when a frequency modulator is used to modulate the frequency of the injection light, the chaotic laser can be suppressed in a stable state, a period-one state, a period-doubling state and quasi-periodic states, respectively, where controlled ranges are found in which the laser can emit a stable light wave or regular pulses. Secondly, if the phase of the injection light is modulated by a phase modulator, the chaotic laser can be stabilized in a period-3 state, a period-4 state and other quasi-periodic states, respectively. Lastly, when the injection light is adjusted by an intensity controller, the laser can be conducted to show all kinds of dynamic behaviors.

Study on the method of controlling chaos in an Er-doped fiber dual-ring laser via external optical injection and shifting optical feedback light

Controlling chaos in an erbium-doped fiber dual-ring laser is studied by injecting an external light and shifting the phase of an optical feedback light. First, the parameters of the externally injected optical signal are adjusted to bring the chaotic laser into a single-period state and a multiperiod state, respectively. In addition, the single-mode locking in a single ring of the laser as well as the dual-mode locking in dual ring of the laser are found. Secondly, the method of optical feedback is used to stabilize chaos by controlling the parameters of the optical devices in an external optical path. We show that the optical negative feedback can stabilize the chaotic laser into a single-period state, while the optical positive feedback can stabilize the chaotic laser into another single-period state and a period-doubling state. Lastly, various dynamical states are produced in the laser by shifting the phase of the optical feedback light.

Period-doubling and quadrupling of bound solitons in a passively mode-locked fiber laser

We report on the experimental observation of regular, period-doubled, period-quadrupled and chaotic states of bound solitons in a passively mode-locked fiber laser. We show that not only the solitons in the laser can easily bind together forming stable states of bound solitons, but also the formed bound solitons as an entity can exhibit complicated nonlinear dynamics, such as the period-doubling route to chaos. Our experimental results further suggest that the bound solitons formed in the laser can have strong binding energy, and consequently behave like ordinary solitons.

Spatial period doubling in Bose-Einstein condensates in an optical lattice

We demonstrate that there exist stationary states of Bose-Einstein condensates in an optical lattice that do not satisfy the usual Bloch periodicity condition. Using the discrete model appropriate to the tight-binding limit we determine energy bands for period-doubled states in a one-dimensional lattice. In a complementary approach we calculate the band structure from the Gross-Pitaevskii equation, considering both states of the usual Bloch form and states which have the Bloch form for a period equal to twice that of the optical lattice. We show that the onset of dynamical instability of states of the usual Bloch form coincides with the occurrence of period-doubled states with the same energy. The period-doubled states are shown to be related to periodic trains of solitons.