Viewpoint Of Nonlinear Dynamics Research Articles

Suppression and frequency control of repetitive spiking in the FitzHugh-Nagumo model.

The FitzHugh-Nagumo equationis a simple model equationthat exhibits spiking. The output signal of a neuron is represented in the spiking frequency or firing rate. We consider a few control methods for spiking from the viewpoint of nonlinear dynamics. The repetitive spiking can be suppressed in the FitzHugh-Nagumo model by the periodic sinusoidal force with high frequency. We study the transition to the suppressed state numerically and perform a linear stability analysis to understand the suppression of the spiking. Next, we study coupled FitzHugh-Nagumo equations. We find that the periodic forcing makes the system chaotic, and the desynchronization induced by chaos weakens the total output of spiking in a certain parameter range. Finally, we propose a method of feedback control for the spiking frequency. We can get the desired spiking and bursting frequency using this feedback control. The feedback control method is analyzed using a mapping for the input.

Nonlinear Dynamic Analysis of Gas Bearing-Rotor System by the Hybrid Method Which Combines Finite Difference Method and Differential Transform Method

Gas bearings have been widely applied to high-speed rotating machines due to their low friction and high rotational speed advantages. Nevertheless, gas lubrication is low viscosity and compressible. It causes the gas bearing-rotor system easy to produce self-excited vibration, which leads to instability of the rotor system and hinders the increase of rotor system speed. It is necessary to study the nonlinear behaviors of the aerostatic bearing-rotor system and the nonlinear vibration of the gas bearing-rotor system, especially considering the distribution mass and flexible and gyroscopic effects of the real rotor. In this paper, the nonlinear behavior of the gas bearing-rotor system is investigated from the viewpoint of nonlinear dynamics. Firstly, the dynamics model of a gas bearing rotor is established by combining the transient Reynolds equation and rotor dynamic equation obtained by finite element method (FEM). The transient Reynolds equation is solved using a hybrid method combining the differential transform method (DTM) and finite difference method (FDM). Then the transient gas force is substituted into the FEM rotor dynamic equation. In the end, based on the bifurcation diagram, the orbit of the rotor center, the frequency spectrum diagram and Poincaré map, the rotor system’s nonlinear behaviors are studied using a solution for the rotor dynamic equation with the Newmark method. Results show that there exists a limited cycle motion in the autonomous rotor system and half-speed whirl in the nonautonomous rotor system.

Long-term trends of regolith movement on the surface of small bodies

This paper studies the long-term migration of disturbed regolith materials on the surface of Solar System small bodies from the viewpoint of nonlinear dynamics. We propose an approximation model for secular mass movement, which combines the complex topography and irregular gravitational field. Choosing asteroid 101955 Bennu as a representative, the global change of the dynamical environment is examined, which presents a division of the creeping-sliding-shedding regions for a spun-up asteroid. In the creeping region, the dynamical equation of disturbed regolith grains is established based on the assumption of “trigger-slide” motion mode. The equilibrium points, local manifolds and large-scale trajectories of the system are calculated to clarify the dynamical characteristics of long-term regolith movement. Generally, we find that for a low spin rate, the surface regolith grains flow toward the middle latitudes from the polar/equatorial regions, which is dominated by the gradient of the geopotential. While spun up to a high rate, regolith grains tend to migrate toward the equator, which happens in parallel with a topological shift of the local equilibrium points at low latitudes. From a long-term perspective, we find the equilibrium points dominate the global trends of regolith movements. Using the methodology developed in this paper, we give a prospect or retrospect to the secular motion of regolith materials during the spin-up process, and the results reveal a significant regulatory role of the equilibrium points. Through a detailed look at the dynamical scheme under different spin rates, we achieve a macro forecast of the global trends of regolith motion during the spin-up process, which explains the global geologic evolution driven by the long-term movements of regolith materials.

Quantitative analysis of fluid transport in dynamic stall of a pitching airfoil using variational Lagrangian coherent structures and lobe dynamics

The evolution of flow structures during dynamic stall of a two-dimensional pitching National Advisory Committee for Aeronautics 0012 airfoil is studied using the variational Lagrangian coherent structures (LCSs), and the mass transport and vorticity transport are precisely analyzed using LCSs and lobe dynamics for further understanding the nature of flow phenomena in dynamic stall. First, the variational LCS algorithm is improved to be efficiently used in the accurate extraction of flow structures. Then, both the hyperbolic LCSs and elliptic LCSs are computed numerically in the whole process of dynamic stall to analyze the evolution of flow structures in detail. Further, a high-accuracy LCS-advection method is used in the advection of LCSs to quantitatively analyze the mass transport and vorticity transport in the evolution of LCSs utilizing lobe dynamics based on nonlinear dynamics. Finally, the evolution and motion of primary leading edge vortex (LEV) and trailing edge vortex (TEV) identified by elliptic LCSs are analyzed in depth. The results obtained can provide a deeper insight into the nature of flow phenomena in dynamic stall from the viewpoint of nonlinear dynamics. Specifically, the nature of evolution of primary LEV and the TEV and the reasons for the changes of lift coefficients are clarified from the viewpoint of fluid transport. To explain it briefly, the variational LCSs and lobe dynamics are powerful tools to quantitatively analyze the evolution of flow structures and fluid transport.

Study on dynamics of vortices in dynamic stall of a pitching airfoil using Lagrangian coherent structures

The evolution of vortex structure and mass transport process during dynamic stall of the two-dimensional pitching NACA0012 airfoil are studied in detail, using Lagrangian coherent structures (LCSs), and the nature of dynamic stall is given from viewpoint of nonlinear dynamics. First, the numerical method with SST k−ω turbulence model is used to simulate the flow field around the pitching oscillation airfoil. Then, the Lagrangian-averaged vorticity deviation (LAVD) method is used to analyze the formation and evolution of vortex structure during dynamic stall. Further, the circulation development process of the primary leading edge vortex (LEV) is studied, with comparison between LAVD method with Q criterion. Finally, the dynamic behaviors, such as the mass transport and evolution of flow structure during the process of dynamic stall, are analyzed in depth by using LCSs, and the fluctuation of lift coefficient and the dynamic stall are investigated from the viewpoint of nonlinear dynamics. The results show that the evolution of vortex structure and mass transport are closely related to the fluctuation of lift coefficient during the dynamic stall, and the low-pressure region formed by vortices and the complex mass transport and mixing process on the suction surface of the airfoil are the main reasons for the high lift during the dynamic stall process. In particular, the primary LEV, which can be accurately identified and tracked by LAVD method, plays a very important role in lift enhancement, and the primary LEV and the secondary LEV form and grow in turn by the intermittent feeding process of shear layer. Additionally, the fluid particles in front of the leading edge of the airfoil enter the LEV through a special mass transport channel, which is textured by LCSs and opened and closed intermittently. More importantly, the saddle point of LCSs is an important component of vortex boundary, and its dynamic behaviors represent the behaviors of vortex. The first separation of saddle point from the shear layer at leading edge indicate the separation of primary LEV from the suction surface of the airfoil, and the occurrence of dynamic stall. The second separation of saddle point from the shear layer at leading edge indicate that primary LEV begins to leave the upper region of the airfoil, corresponding to a sharp drop in lift coefficient. Generally, compared to the traditional visualization techniques, the Lagrangian analysis based on LCSs and LAVD can provide a deeper insight into the dynamics of the vortex in flow field around pitching oscillation airfoil and the dynamic mechanism of dynamic stall.

Switching thresholds for multistable systems under strong external perturbation

Multistability is a common feature of various dynamical systems which manifests itself as the possibility to demonstrate various behaviors for the same parameter values. These behaviors or states of the system must be stable against weak perturbation in order to be observable in real life. However, a strong enough perturbation may destroy a certain state and lead to the system switching to another one. From the viewpoint of nonlinear dynamics, the response of a multistable system to a strong stimulus depends on the configuration and the mutual arrangement of basins of different attractors. In the present paper, we introduce a novel measure for characterization of a multistable system, the switching threshold. It equals the amplitude of a minimal perturbation capable of switching the system from one attractor to another. We develop a numerical algorithm for calculation of the switching thresholds and apply it to a number of paradigmatic models including dynamical networks. We show that the values of switching thresholds provide important information about multistable systems and their responses to external stimuli. This information allows to develop methods of optimal control of multistable systems by external signals. Surprisingly, it also allows to predict some features of their dynamics under the influence of external noise.

Devil’s staircases in a thermoacoustic system with sinusoidal excitations

The influences of sinusoidal excitations on a Rijke tube system through the introduction of nonlinear dynamics are investigated in detail. The system is governed by one-dimensional partial differential equations, which are addressed by means of the Galerkin procedure and analysed from the viewpoint of nonlinear dynamics. The results show a rich variety of behaviours in the system, including subcritical bifurcation, hysteresis and phase locking. In certain parameter ranges, the solution switches between periodic and quasi-periodic. These ranges mainly depend on the intensity of the heat source in the tube. The phase-locking intervals that correspond to periodic solutions compose a devil’s staircase, whose Lebesgue measure increases as the amplitude of the excitation increases.

Delays in perception and action for improving walk–run transition stability in bipedal gait

This paper focuses on a transition motion between bipedal walking and running, whose characteristics have been revealed through numerous biological experiments. Although hysteresis in walk-to-run and run-to-walk transitions, the amount of which is proportional to the magnitude of acceleration/deceleration, is observed, it has not been elucidated yet. This is due to difficulty to conduct any biological experiments without the hysteresis in locomotion. From the viewpoint of nonlinear dynamics, the hysteresis is caused by dependency of the state history. Delays in perception and action for the walk–run transition can be assumed as the cause of the hysteresis. This paper therefore investigates i) whether the delays really cause the hysteresis in the walk–run transition, and ii) how they contribute to locomotion performance. To this end, in numerical simulations, we employ a controller for bipedal gait, named unified bipedal gait (UBG), which has capabilities of walking, running, and transitions between them like bipeds do. UBG is first optimized in pursue of biologically plausible controller with the same characteristics about the transition motion for reliable investigation. This optimized UBG reveals that the delays in perception and action actually cause the hysteresis with linearity of its amount and the magnitude of acceleration/deceleration. In addition, the delays play the key role of a bridge between latent representations of walking and running, thereby improving the success rate of the transition by nearly 40% from the case without the delays.

On synchronization in flow over airfoil with local oscillating flexible surface at high angle of attack using Lagrangian coherent structures

Lagrangian coherent structures (LCSs) are used to reveal the mechanism of high-lift airfoil with local oscillating at high angle of attack, as the frequency of local oscillation is synchronized with the characteristic frequency of the flow field. First, the forced excitation is used to control the oscillation of the local flexible surface, and the fluid-structure interaction model composed by local oscillating airfoil and unsteady fluid is established. Then, the unsteady flow around a 2-D local oscillating airfoil at high angle of attack is simulated and analyzed numerically by commercial software Fluent with the UDF function and the dynamic grid technique. The results show that the local oscillation can improve the lift of the airfoil. Moreover, as the frequency of the local oscillation is synchronized with the characteristic frequency of the flow field around the rigid airfoil, the lift could be enhanced significantly. Finally, the LCSs are introduced to study the mass transport between main flow and separation area as the frequency of local oscillation is synchronized with the characteristic frequency of flow field, from viewpoint of nonlinear dynamics. It is found that the stable manifolds and unstable manifolds are tangled with each other as time goes on, inducing the mass transport between the main flow and the separating area in a periodical way.

Similarity and vortex-acoustic lock-on behavior in thermoacoustic oscillation involving vortex shedding

In engineering, the combustion chamber with a backward step is very popular, and it is a kind of flame stabilizer. In this type of combustion chamber, there will be shedding vortices at the step due to the instability of the flow field. The shedding vortices will carry reactants to move downstream and burn, resulting in unstable heat release and then pressure and velocity fluctuations of the sound field, thereby, finally, forming a combustion-vortex-acoustic interaction process. If a positive feedback loop is formed between the unstable heat release and the pressure fluctuation of sound field, combustion instability will occur, and it is also referred to as thermoacoustic oscillation due to vortex shedding. Combustion instability frequently occurs in many practical systems or equipment, and its induced significant pressure oscillations have a serious influence on the normal operation of the equipment. Recently, the combustion instability has been extensively studied experimentally, but the theoretical investigation on its nature is still rare. Since combustion instability is a complicated nonlinear phenomenon, it is necessary to study its nature from the viewpoint of nonlinear dynamics. Based on the one-dimensional simplified model of thermoacoustic instability involving vortex shedding proposed by Matveev and Culick, the typical nonlinear phenomenon in thermoacoustic oscillation induced by vortex shedding is studied. The study focuses on the initial value sensitivity of the system, the influence of key parameters on thermoacoustic oscillation, and the phenomenon of vortex-acoustic lock-on. Firstly, the Galerkin method is used to approximate the governing equation, and the partial differential equations are reduced to a set of ordinary differential equations. Then, the first ten modes are selected, and the pressure and velocity fluctuations of sound field under different system parameters are obtained by MATLAB program. Finally, the thermoacoustic instability of the system under different initial disturbances, the influences of different steady flow velocity on the thermoacoustic oscillation of the system, and the phenomenon of vortex-acoustic lock-on in thermoacoustic oscillation are studied in detail. The results show that the system of thermoacoustic oscillation involving vortex shedding is extremely sensitive to initial values, and there are a rich variety of nonlinear phenomena. With steady flow velocity increasing, the amplitude of pressure fluctuation augments generally. However, the similar structures are found in several intervals of steady flow velocity, and the amplitude first decreases and then increases. In particular, it is verified that the system oscillates periodically by integer (fp/fs) multiple of the vortex impinging frequency (fs), that is, the vortex-acoustic frequency locking with the number of revolutions fp/fs, which is found in experiment and can be regarded as an important characteristic of periodic thermoacoustic oscillation.

Initial State Dependent Nonsmooth Bifurcations in a Fractional-Order Memristive Circuit

In this paper, Chua’s circuit model with a fractional-order memristor is proposed and investigated from the viewpoint of nonlinear dynamics. Unlike the previous fractional-order models as generalizations of integer-order memristive Chua’s circuit in the literature, by replacing all the first-order derivatives in the system equation with fractional-order derivatives, the proposed model has only one fractional-order derivative in the system equation, introduced on the basis of a physical observation. Stability and bifurcation are analyzed for a sub-system, and numerical simulation is done for the whole circuit system. “Intermittent chaos” resulting from tangent bifurcation or grazing bifurcation is found numerically, for which limit cycle and chaotic attractor switch with very high frequency. This is a typical feature of nonsmooth dynamic systems, and the nonsmoothness is caused mainly by the fractional-order derivative.

Nonlinear Modeling and Dynamic Analyses of the Hydro–Turbine Governing System in the Load Shedding Transient Regime

Load shedding processes are widespread in hydropower stations, which has great influence on the safe and stable operation of the hydro–turbine governing system. In order to study the dynamic characteristics of the hydro–turbine governing system during the load shedding process, a novel nonlinear mathematical model of the hydro–turbine governing system is established considering the hydro–turbine system, the generator system and the governor system. In particular, a novel nonlinear mathematical model of the six hydro–turbine transfer coefficients is presented based on the definitions and hydro–turbine internal characteristics. After that, from the viewpoint of nonlinear dynamics and the practical engineering, the dynamic characteristics of the hydro–turbine governing system are investigated utilizing bifurcation diagrams, time series, Poincare maps, power spectrums and phase planes. Some meaningful results are found. The advantages of the novel nonlinear mathematical model are illustrated and commented in detail in comparison with the previous model. Finally, these models and analysis results will provide some theoretical references for the operation of hydropower stations in the load shedding transient.

A new look to coma from the viewpoint of nonlinear dynamics

In this work, we propose a simple nonlinear network of consciousness that demonstrates how the trauma to the ascending reticular formation could lead to coma. Studies show that the healthy brain works at the edge of chaos. Coma, as a disorder, is a stable state that the inherently chaotic brain could trap in. There are several brain areas playing a critical role in consciousness. A trauma to each of these areas could lead to disruption of conscious experience. Ascending reticular formation, which plays a key role in consciousness, is the focus area of this work. We study the effect of trauma on the connection between the reticular formation and the rest of consciousness network that could lead to stable behavior of the brain, i.e. coma. The effect of increased inhibitory neurotransmitter on the occurrence of unconsciousness is displayed as well. We also show how a local boost would affect a brain in the coma.

Resonances and multistability in a Josephson junction connected to a resonator.

We study the dynamics of a Josephson junction connected to a dc current supply via a distributed parameter capacitor, which serves as a resonator. We reveal multistability in the current-voltage characteristic of the system; this multistability is related to resonances between the generated frequency and the resonator. The resonant pattern requires detailed consideration, in particular, because its basic features may resemble those of patterns reported in experiments with arrays of Josephson junctions demonstrating coherent stimulated emission. From the viewpoint of nonlinear dynamics, the resonances between a Josephson junction and a resonator are of interest because of the specificity of the former; its oscillation frequency is directly governed by control parameters of the system and can vary in a wide range. Our analytical results are in good agreement with the results of numerical simulations.

Sudden Cardiac Death from the Perspective of Nonlinear Dynamics

There are some reports that sympathetic nerve activity (SNA) shows a characteristic pattern a few hours before the onset of lethal ventricular arrhythmias. If so, it could be possible to predict sudden cardiac death a few hours in advance of its occurrence. Recently, we reported that a previously unidentified V-trough of SNA is a potential precursor of lethal cardiac events by examining 24-hour ambulatory electrocardiograms in which such an event was recorded by chance. In contrast, the chaotic nature of heart rate variability has been noted recently from the viewpoint of nonlinear dynamics. This study models the hemodynamics, consisting of heart rate, SNA, and blood pressure (BP), by modifying a known chaotic electrical circuit, the Chua circuit. A V-trough of the SNA appears when the resistive element between the SNA and BP in the circuit is increased, which corresponds to the impaired regulation of BP by the SNA. This finding is consistent with an acknowledged finding that a depressed baroreflex (a reflex of the BP by SNA) may trigger a lethal arrhythmia. This study indicates that a V-trough of the SNA is a possible precursor of sudden cardiac death on the basis of experimental and clinical findings as well as mathematical modeling.

Nonlinear dynamics, seismic activity and aerospace sounding systems

Processes and phenomena are under consideration, which can be realized from the viewpoint of nonlinear dynamics and are typical for geosystems. Attention is focused on the main features and new possibilities given by the ideas and approaches of nonlinear dynamics for solving applied problems of geophysics. Premises for physical interpretation of spontaneous electromagnetic and seismoacoustic emission as a product of temporally uninterrupted transitional dynamic processes related to interaction of different subsystems of geo-medium as its metastable conditions and succession of such conditions are analyzed. An attempt has been undertaken to analyze lithosphere-atmosphere-ionosphere relations, methods of multiparametric aerospace monitoring of short-term precursors of strong seismic events. Its possibilities and limits are considered and the necessity of integrating passive monitoring systems based on the study of medium-generated emission signals spectra with active ones, oriented to system receptivity control. Baselessness of attempts to give reliable and accurate short-term forecast without studying physics of producing destruction sources and development of deformation process within the Earth’s crust during the final stage in a regime with intensification has been noticed.

Study on Mass Transports in Evolution of Separation Bubbles Using LCSs and Lobe Dynamics

AbstractThe lobe dynamics andmass transport between separation bubble and main flow in flow over airfoil are studied in detail, using Lagrangian coherent structures (LCSs), in order to understand the nature of evolution of the separation bubble. For this problem, the transient flow over NACA0012 airfoil with low Reynolds number is simulated numerically by characteristic based split (CBS) scheme, in combination with dual time stepping. Then, LCSs and lobe dynamics are introduced and developed to investigate themass transport between separation bubble and main flow, from viewpoint of nonlinear dynamics. The results show that stable manifolds and unstable manifolds could be tangled with each other as time evolution, and the lobes are formed periodically to induce mass transport between main flow and separation bubble, with dynamic behaviors. Moreover, the evolution of the separation bubble depends essentially on the mass transport which is induced by lobes, ensuing energy and momentum transfers. As the results, it can be drawn that the dynamics of flow separation could be studied using LCSs and lobe dynamics, and could be controlled feasibly if an appropriate control is applied to the upstream boundary layer with high momentum.

Bifurcation Behavior in Oscillations during H2O2 Reduction at Pt Electrodes

Electrochemical oscillations are of interest from the viewpoint of dynamic self-organization of molecular systems. Extensive studies have revealed that N-shaped negative differential resistance (N-NDR) plays an essential role in the majority of the oscillations because an N-NDR induces a positive feedback mechanism. Simple periodic oscillations are explained by the combination of a positive feedback loop and a negative one, latter of which involves a slow process such as the surface concentration of an electroactive species and the surface coverage of an adsorbed species [1]. Among the electrochemical oscillations, the reduction of H2O2 at Pt electrodes in H2SO4 solutions (H2O2 + 2H+ + 2e- → 2H2O) has an especially unique feature because it exhibits ten kinds of oscillations, as we have reported before [2]. One of the oscillations, named oscillation A, appeared in the potential region where under-potential deposited H (upd-H), which suppressed the H2O2 reduction, was formed on Pt surface (see Figure 1a). Another oscillation, named oscillation D, appeared when a small amount of Br- ions, which adsorbed on Pt surface, was added to the solutions. The reduction of S2O8 2- at Pt electrodes in acidic solutions (S2O8 2- + 2e- → 2 SO4 2-) was also unique because it showed several kinds of oscillations. The formation of upd-H also suppressed the S2O8 2- reduction; hence one of the oscillations, named oscillation a, appeared in the potential region of upd-H [3]. The electrochemical oscillations are also of interest from the viewpoint of nonlinear dynamics because they often exhibit transitions among non-oscillatory state, periodic oscillations, quasi-periodic ones, mixed-mode ones, and chaotic ones via period-adding bifurcation, period-doubling bifurcation, and so on. We have been studying bifurcation behavior in the oscillations during the H2O2 and S2O8 2- reductions. The studies showed [3,4] that the complex oscillations such as period-n, mixed-mode, and chaotic oscillations were observed when oscillation A appeared simultaneously with oscillation a (or D) though each was period-1 oscillation (see Figure 1b for the chaotic oscillation induced by the simultaneous occurrence of oscillations A and a). Furthermore, the studies led us to the conclusion that the complex oscillations appeared when two kinds of simple periodic oscillations occurred at the same time, and also that they were caused by the interplay among a positive feedback loop and two negative feedback loops. Recently, we found [5] that oscillation A changed into the complex oscillations when inorganic salts such as Na2SO4 and K2SO4 are added to the solutions (see Figure 1c for the chaotic oscillation). The solutions originally contained (bi)sulfate ions dissociated from H2SO4, and hence we explained that alkali metal ions, i.e., Na+ and K+ ions, caused a negative feedback loop that induced the complex oscillations. This presentation will show the bifurcation behavior in detail and also provide a definitive factor for the appearance of the complex oscillations. REFERENCES [1] M. Orlik, Self-Organization in Electrochemical Systems I, Springer, Berlin, 2012. [2] Y. Mukouyama, H. Kawasaki, D. Hara, M. Kikuchi, Y. Yamada, S, Nakanishi, ECS Trans., 69 (39) 37-45, 2015. [3] Y. Mukouyama, H. Kawasaki, D. Hara, S. Nakanishi, J. Solid State Electrochem., 19, 3253-3263, 2015. [4] Y. Mukouyama, M. Kikuchi, H. Okamoto, J. Solid State Electrochem., 9, 290-295, 2005. [5] Y. Mukouyama, D. Hara, H. Kawasaki, M. Kikuchi, Y. Yamada, S, Nakanishi, ECS Trans., 69 (39) 47-57, 2015. FIGURE CAPTION Figure 1. The I – E curves for a Pt-disc electrode in 0.1 M H2SO4 + 0.2 M H2O2 (a) without Na2S2O8 nor Na2SO4, (b) with 0.1 M Na2S2O8, and (c) with 0.2 M Na2SO4, measured under potential-controlled conditions. The insets in panels a, b, and c are the waveforms of oscillations observed at −0.065, −0.070, and −0.085 V, respectively. Figure 1

Dynamical behavior and peak power reduction in a pair of energy storage oscillators coupled by delayed power price.

This paper investigates dynamics of a management system for controlling a pair of energy storages. The system involves the following two characteristics: each storage behaves in a manner that reduces the number of charge noncharge cycles and begins to be charged when the price of power is lower than a particular price threshold. The price is proportional to the past total power flow from a power grid to all storages. A peak of the total power flow occurs when these storages are charged simultaneously. From the viewpoint of nonlinear dynamics, the energy storages can be considered as relaxation oscillators coupled by a delay connection. Our analytical results suggest that the peak can be reduced by inducing an antiphase synchronization in coupled oscillators. We confirm these analytical results through numerical simulations. In addition, we numerically investigate the dynamical behavior in 10 storages and find that time delay in the connection is important in reducing the peak.

Chaotic Oscillations in H2O2 - H2so4 - Pt Electrochemical System

INTRODUCTION Electrochemical oscillations are of interest from the viewpoint of dynamic self-organization of molecular systems. Extensive studies have revealed that an N-shaped negative differential resistance (N-NDR) plays an essential role in the majority of the oscillations. Simple periodic oscillations are explained by the interaction between a positive feedback loop due to an N-NDR characteristic and a negative one where a slow process is involved [1]. Electrochemical oscillations are also of interest from the viewpoint of nonlinear dynamics because they sometimes exhibit chaotic oscillations. Our group has reported that chaotic oscillations appear when two kinds of simple periodic oscillations, named oscillation A and oscillation α, occur simultaneously [2]. Oscillation A (or α) appeared during the reduction of H2O2 (or S2O8 2- dissociated from Na2S2O8) at Pt electrodes in strong acidic solutions such as H2SO4 and HClO4 electrolytes. We concluded that the chaotic oscillations were caused by the interplay among a positive feedback loop due to an N-NDR characteristic, a negative feedback loop where the surface concentration of H2O2 was involved, i.e., that for oscillation A, and a negative feedback loop where the surface concentration of S2O8 2−was involved, i.e., that for oscillation α. On the other hand, the H2O2 reduction at Pt electrodes in H2SO4 solutions was affected by the salts such as Na2SO4 and K2SO4 because the alkali metal ions, Na+ and K+, decreased the electromigration transport of H+ ions from the solution bulk to the electrode surface [3]. Recently, oscillation A was found to appear as a chaotic oscillation in the presence of Na2SO4, indicating that Na+ ions caused a negative feedback loop that induced the chaotic oscillation. In this presentation, the conditions for the appearance of the chaotic oscillation will be discussed. Although the chaotic oscillations due to the simultaneous occurrence of oscillations A and α were also observed in the solutions that contained Na+ ions, they were not induced by Na+ions, which will also be discussed. RESULTS and DISCUSSION Figure 1 shows the current (I) – potential (E) curves for a Pt-disc electrode. When the solution was 0.1 M H2SO4 + 0.2 M H2O2 (Fig. 1a), the H2O2 reduction occurred in the potential region below ca. 0.8 V, and oscillation A appeared at potentials around –0.075 V (vs. SHE) where an N-NDR characteristic appeared. The hydrogen evolution reaction occurred in the potential region below ca. –0.1 V. Oscillation A was simple and periodic as shown in the inset of Fig. 1a. When the solution contained 0.2 M Na2SO4 (Fig. 1b), an aperiodic oscillation, which could be judged as a chaotic oscillation by plotting a next-minimum return map, appeared as shown in the inset. The current values of the higher turning points were almost constant, whereas those of the lower ones were irregular. This indicates that the negative feedback loop for oscillation A played a role in the higher turning points, and also that not only the loop but also another negative feedback loop which was induced by Na+ ions worked in the lower turning points. The chaotic oscillation appeared only when the concentration of Na2SO4 was approximately 0.2 M, and thus the negative feedback loop was induced only when the concentration of Na+was approximately 0.4 M. When the solution contained 0.1 M Na2S2O8 (Fig. 1c), the reduction of S2O8 2− occurred below ca. 0.5 V though the current due to the reduction was too small to affect the I – E curve, and a chaotic oscillation also appeared as shown in the inset [2]. The values of the higher turning points and those of the lower ones were irregular, indicating that two negative feedback loops played roles both in the higher turning points and the lower ones. The loop induced by Na+ ions did not work in higher ones, nor in the lower ones when the Na+ concentration was 0.2 M. We can thus say that the chaotic oscillation was not caused by Na+ions. REFERENCES [1] M. Orlik, Self-Organization in Electrochemical Systems I, Springer, Berlin (2012). [2] Y. Mukouyama, H. Kawasaki, D. Hara, S. Nakanishi, J. Solid State Electrochem., DOI 10.1007/s10008-015-2813-z. [3] Y. Mukouyama, M. Hasegawa, S, Nakanishi, ECS Trans., 64 (2014) accepted. FIGURE CAPTION Figure 1. The I – E curves for a Pt-disc electrode in 0.1 M H2SO4 + 0.2 M H2O2 (a) without Na2SO4 nor Na2S2O8, (b) with 0.2 M Na2SO4, and (c) with 0.1 M Na2S2O8, measured under potential-controlled conditions. The insets in panels a, b, and c are the waveforms of oscillations observed at −0.065, −0.085, and −0.070 V, respectively. Figure 1