Multistable Oscillation Research Articles

Bifurcation analysis and nonlinear dynamics of a rolling magnet multistable electromagnetic energy harvester

The objective of this study is to provide a rolling magnet multistable electromagnetic-induction energy harvester (RM-MEH) for scavenging energy from a wide frequency range. The RM-MEH designed based on a magnetic levitation rolling magnet possesses the merit of small damping. By clarifying the mechanics of the RM-MEH, the static bifurcation behavior is investigated and results demonstrate that monostable, bistable, and tristable configurations with different types of potentials can be obtained with proper parameters. Numerical simulations under sweep frequency excitation indicate that the monostable, bistable, and tristable configurations with proper potential functions achieve large-amplitude oscillation in a wide frequency range. Under constant frequency excitation, the nonlinear dynamics are analyzed utilizing the bifurcation diagram, phase orbit, and Poincaré map, and the multiple vibrational patterns are verified. Finally, the vibration isolation characteristics of the system are briefly discussed considering the electromagnetic force of the RM-MEH. In summary, the demonstration of the novel RM-MEH expands the approach to achieving multistable oscillation and provides a new way of thinking for designing nonlinear energy harvesters.

Multistable autonomous motion of fruit on a smooth hotplate

Origin of scale coupling may be clarified by the understanding of multistability, or shifts between stable points via unstable equilibrium points due to a stimulus. When placed on a glasstop hotplate, cobs of corn underwent multistable autonomous oscillation, with unsteady viscous lubrication below and transitional plumes above, where the buoyancy to inertia force ratio is close to ≥ 1.0. Subsequently, viscous wall-frictional multistability occurred in six more types of smooth fruit with nominal symmetry. Autonomous motion observed are: cobs roll, pitch and yaw; but green chillies, blueberries, tropical berries, red grapes, oblong grapes and grape tomatoes roll and yaw. The cross products of the orthogonal angular momentum produce the observed motion. The prevalence of roll and yaw motion are the most common. Lubricant film thickness hproptoU/(TF), for cob mass F, tangential velocity U and temperature T. In heavier cobs, the film thins, breaking frequently, changing stability. Lighter cobs have high h, favoring positive feedback and more spinning: more T rises, more viscosity of water drops, increasing U and h more, until cooling onsets. Infrequent popping of the tender corn kernel has the same mean sound pressure level as in hard popcorn. The plume vortex jets lock-in to the autonomous rolling cob oscillation. Away from any solid surface, the hot-cold side boundary produces plumes slanted at ± 45°. Surface fencing (13–26 μm high) appears to control motion drift.

Temporally Targeted Interactions With Pathologic Oscillations as Therapeutical Targets in Epilepsy and Beyond.

Self-organized neuronal oscillations rely on precisely orchestrated ensemble activity in reverberating neuronal networks. Chronic, non-malignant disorders of the brain are often coupled to pathological neuronal activity patterns. In addition to the characteristic behavioral symptoms, these disturbances are giving rise to both transient and persistent changes of various brain rhythms. Increasing evidence support the causal role of these “oscillopathies” in the phenotypic emergence of the disease symptoms, identifying neuronal network oscillations as potential therapeutic targets. While the kinetics of pharmacological therapy is not suitable to compensate the disease related fine-scale disturbances of network oscillations, external biophysical modalities (e.g., electrical stimulation) can alter spike timing in a temporally precise manner. These perturbations can warp rhythmic oscillatory patterns via resonance or entrainment. Properly timed phasic stimuli can even switch between the stable states of networks acting as multistable oscillators, substantially changing the emergent oscillatory patterns. Novel transcranial electric stimulation (TES) approaches offer more reliable neuronal control by allowing higher intensities with tolerable side-effect profiles. This precise temporal steerability combined with the non- or minimally invasive nature of these novel TES interventions make them promising therapeutic candidates for functional disorders of the brain. Here we review the key experimental findings and theoretical background concerning various pathological aspects of neuronal network activity leading to the generation of epileptic seizures. The conceptual and practical state of the art of temporally targeted brain stimulation is discussed focusing on the prevention and early termination of epileptic seizures.

Resilience of networks of multi-stable chaotic systems to targetted attacks

We investigate the collective dynamics of chaotic multi-stable Duffing oscillators connected in different network topologies, ranging from star and ring networks, to scale-free networks. We estimate the resilience of such networks by introducing a variant of the concept of multi-node Basin Stability, which allows us to gauge the global stability of the collective dynamics of the network in response to large perturbations localized on certain nodes. We observe that in a star network, perturbing just the hub node has the capacity to destroy the collective state of the entire system. On the other hand, even when a majority of the peripheral nodes are strongly perturbed, the hub manages to restore the system to its original state. This demonstrates the drastic effect of the centrality of the perturbed node on the collective dynamics of the full network. Further, we explore scale-free networks of such multi-stable oscillators and demonstrate that targetted attacks on nodes with high centrality can destroy the collective dynamics much more efficiently than random attacks, irrespective of the nature of the nodal dynamics and type of perturbation. We also find clear evidence that the betweeness centrality of the perturbed node is most crucial for dynamical robustness, with the entire system being more vulnerable to attacks on nodes with high betweeness. These results are crucial for deciding which nodes to stringently safeguard in order to ensure the recovery of the network after targetted localized attacks.

Describing dynamics of driven multistable oscillators with phase transfer curves.

Phase response curve is an important tool in the studies of stable self-sustained oscillations; it describes a phase shift under action of an external perturbation. We consider multistable oscillators with several stable limit cycles. Under a perturbation, transitions from one oscillating mode to another one may occur. We define phase transfer curves to describe the phase shifts at such transitions. This allows for a construction of one-dimensional maps that characterize periodically kicked multistable oscillators. We show that these maps are good approximations of the full dynamics for large periods of forcing.

Coexisting Behaviors of Asymmetric Attractors in Hyperbolic-Type Memristor based Hopfield Neural Network.

A new hyperbolic-type memristor emulator is presented and its frequency-dependent pinched hysteresis loops are analyzed by numerical simulations and confirmed by hardware experiments. Based on the emulator, a novel hyperbolic-type memristor based 3-neuron Hopfield neural network (HNN) is proposed, which is achieved through substituting one coupling-connection weight with a memristive synaptic weight. It is numerically shown that the memristive HNN has a dynamical transition from chaotic, to periodic, and further to stable point behaviors with the variations of the memristor inner parameter, implying the stabilization effect of the hyperbolic-type memristor on the chaotic HNN. Of particular interest, it should be highly stressed that for different memristor inner parameters, different coexisting behaviors of asymmetric attractors are emerged under different initial conditions, leading to the existence of multistable oscillation states in the memristive HNN. Furthermore, by using commercial discrete components, a nonlinear circuit is designed and PSPICE circuit simulations and hardware experiments are performed. The results simulated and captured from the realization circuit are consistent with numerical simulations, which well verify the facticity of coexisting asymmetric attractors' behaviors.

Stochastic switching between multistable oscillation patterns of the Min-system

The spatiotemporal oscillation patterns of the proteins MinD and MinE are used by the bacterium E. coli to sense its own geometry. Strikingly, both computer simulations and experiments have recently shown that for the same geometry of the reaction volume, different oscillation patterns can be stable, with stochastic switching between them. Here we use particle-based Brownian dynamics simulations to predict the relative frequency of different oscillation patterns over a large range of three-dimensional compartment geometries, in excellent agreement with experimental results. Fourier analyses as well as pattern recognition algorithms are used to automatically identify the different oscillation patterns and the switching rates between them. We also identify novel oscillation patterns in three-dimensional compartments with membrane-covered walls and identify a linear relation between the bound Min-protein densities and the volume-to-surface ratio. In general, our work shows how geometry sensing is limited by multistability and stochastic fluctuations.

Synchronization of intermittent behavior in ensembles of multistable dynamical systems.

We propose a methodology to analyze synchronization in an ensemble of diffusively coupled multistable systems. First, we study how two bidirectionally coupled multistable oscillators synchronize and demonstrate the high complexity of the basins of attraction of coexisting synchronous states. Then, we propose the use of the master stability function (MSF) for multistable systems to describe synchronizability, even during intermittent behavior, of a network of multistable oscillators, regardless of both the number of coupled oscillators and the interaction structure. In particular, we show that a network of multistable elements is synchronizable for a given range of topology spectra and coupling strengths, irrespective of specific attractor dynamics to which different oscillators are locked, and even in the presence of intermittency. Finally, we experimentally demonstrate the feasibility and robustness of the MSF approach with a network of multistable electronic circuits.

Numerical Study on Multi-Stable Oscillations of Woodwind Single-Reed Instruments

Single reed instruments with cylindrical and conical bores were studied numerically, focusing on the dependence of the acoustic mechanism on the bore geometry. As experimentally demonstrated by Idogawa et al. [J. Acoust. Soc. Am., Vol.98, p.540 (1993)], reed instruments can be characterized as multi-attractor systems, which exhibit multi-stable oscillations and hysteretic transitions among oscillating states with change of a control parameter, such as blowing pressure in the mouth. We numerically analyzed dynamical models of single reed instruments to clarify differences in the acoustic mechanisms between cylindrical and conical bore instruments. We analyzed a dynamical model of a cylindrical pipe fitted with a clarinet mouthpiece(CPCM), as a simplified model of the clarinet, and a dynamical model of a truncated cone with a clarinet mouthpiece (TCCM), as a model of conical-bore instruments, together with intermediately shaped models. We found a clear difference in the global structure of transition diagrams (i.e., the overall picture showing the transitions among all the excited states with change of the blowing pressure) between CPCM and TCCM, together with interesting structural changes of the transition diagrams in the intermediate models.

Bubble response to the amplitude modulation signal near the threshold of dynamical stability

There is a range of acoustic techniques for characterizing bubble populations within liquids [Leighton et al., Ultrasonics 34, 661–667 (1996)]. The linear resonant backscattering was the first detection technique. The great difference between the compressibility of gas in the bubble and surrounding liquid leads to the easy manifestation of nonlinear effects, the simplest of which is the presence of harmonics at 2ωp, 3ωp, etc., of the pure tone driving frequency ωp in the scattering signal. However, bubble pulsation of finite amplitude results not only in the harmonics generation. The nonlinear resonance characterized by multistable oscillation states arising from the saddle-node bifurcations is a significant example. The emphasis of this study is to propose a technique for bubble sizing by using the ability of a bubble as a nonlinear oscillatory system to amplify weak signals near the threshold of dynamical stability. The analytical as well as numerical solutions have been derived for the nonlinear bubble response to the modulation driving pressure. The magnitude and the form of the acoustical signal reradiated near the threshold of dynamical stability are drastically different from the modulation of incident wave and enable the characterization of the bubble population in liquid.

Oscillation mode selection using bifurcation of chaotic mode transitions in a nonlinear ring resonator

This paper demonstrates the effectiveness of an adaptive parametric control method for searching and switching among a large number of multistable oscillation modes using chaotic mode transitions. The adaptive control is used to select nonlinear oscillation modes in an electro-optic ring resonator. In the adaptive control scheme, the result of a simple test of resonator output is fed back to a single parameter, pump laser power, governing bifurcation to and from chaos. The test is the presence or absence of a target code in the oscillation waveform of the resonator output. Chaotic mode transition phenomena, called chaotic itinerancy, are investigated in terms of code dynamics, and the results are used to determine the optimal parameters for the adaptive control.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Storage of optical pulse data sequences in loop memory using multistable oscillations

A new configuration for a loop memory using multistable nonlinear oscillation modes was proposed. The basic functions of the proposed loop memory have been confirmed with experimental demonstration of ‘write’ and ‘erase’ using optical pulse sequences in an electro-optical hybrid nonlinear ring resonator.