Tristable State Research Articles

Simplicial epidemic model with a threshold policy

We establish a simplicial empty-susceptible–infected (ESI) model with consideration of threshold policy to depict the network-based epidemic transmission, where the underlying propagation structures are expanded from edges to higher-order structures. To address the epidemic evolution in an explicit network, we formulate the quenched mean-field probability evolution about each site, which is composed of non-smooth differential equations based on network topology. Remarkably, under the combined action of non-smooth and high-order structures, a tristable state is observed in empirical social networks, which is consistent with the coexistence of three stable equilibria by analysis of the mean-field system. Moreover, we find that a sliding mode exists in empirical social networks, which is also indicated by the theoretical analysis of the mean-field probability equations. Finally, the system is divided into the free subsystem without the threshold policy and control subsystem with the threshold policy. Both subsystems admit a stable disease-free equilibrium and a stable endemic equilibrium, as well as coexistence of a stable disease-free equilibrium and a stable pseudo equilibrium in the system, thereby admitting three types of the bistable state under the policy with different critical levels.

Modeling and Evaluation of a Multi-Stable Hybrid Energy Harvester

This article develops a multi-stable hybrid energy harvester (MSHEH) which consists of a piezoelectric energy harvester (PEH) and an electromagnetic energy harvester (EMEH). By tuning two parameters, the MSHEH can achieve a mono-stable, bi-stable, and tri-stable state, respectively. A numerical procedure is developed to compute the EMEH’s transduction factor. The obtained result is validated experimentally. Using the equivalent magnetic 2-point dipole theory, the restoring force model of the magnetic spring is established. The obtained model is verified experimentally. The energy harvesting performances of the MSHEH under the four different configurations (linear, mono-stable, bi-stable and tri-stable) subjected to frequency sweep excitations are evaluated by simulation and validated by experiment. The comparative analysis focuses on power output, accumulated harvested energy, and effective energy-harvesting bandwidth. The optimum load resistances are investigated by Pareto front optimizations. The following key findings are obtained. When subjected to high-level frequency sweep excitation, the tri-stable configuration exhibits the widest frequency bandwidth and the highest total accumulated harvested energy. When subjected to low-level frequency sweep excitation, the bi-stable configuration is more efficient in energy harvesting. The best performance trade-off between the PEH and EMEH can be achieved by selecting the optimum load resistances properly.

Theoretical and experimental study of a stable state adjustable nonlinear energy sink

Due to high sensitivity to the changes in external excitation intensity, the implementation of nonlinear energy sinks (NESs) have been greatly limited in practical applications. This study presents a stable state adjustable NES (SA-NES) structure. By adjusting the structural geometric relationship, the SA-NES structure can easily switch its stable state among monostable, bistable, and tristable. The governing equation of the coupled system is obtained by Hamilton's principle. The approximate analytical solution is obtained by the harmonic balance method, and the slow invariant manifold is obtained complexification-averaging method, which are validated through numerical analysis. Through theoretical analysis and experimental validation, the dynamic response of the SA-NES and vibration reduction performance are studied under different levels of excitations. The obtained results show that the designed SA-NES can effectively suppress the vibration under different level excitation intensities. It is also shown that the SA-NES structure can be adjusted to the monostable state, and the vibration of the linear oscillator can be effectively suppressed by the strong modulation response under a certain excitation intensity. When the excitation intensity is weak or strong, the SA-NES can be adjusted to the bistable state and the tristable state, respectively, thus effectively suppressing the vibration through chaotic inter-well oscillation. This study reveals the vibration suppression mechanism of the SA-NES, and introduces a new NES configuration to suppress different levels of engineering excitations.

Harvest more bridge vibration energy by nonlinear multi-stable piezomagnetoelastic harvester

The idea of using bridge vibration energy to power node sensors is promising in solving the power problems of bridge health monitoring systems. This study proposes a piezomagnetoelastic harvester that tries utilizing nonlinear multi-stability to improve the harvesting performance of bridge vibration energy. The harvester can exhibit multi-stable behaviors due to the introduced nonlinear forces. The potential energy functions are derived and corresponding analyzes are carried out. The results show that the tri-stable state of harvester can be obtained by adjusting the parameters related to magnetic forces. Its potential barriers are low and the distance between potential wells is large, so it can execute snap-through motion easily. The experimental study was carried out for different vehicle speeds. The results verify that the energy harvester in a tri-stable state can generate the largest electric output over a wide range of vehicle speeds. Moreover, it is proved that the tri-stable state can protect the harvester from excessive deformation and subsequent damage. Therefore, the tri-stable configuration has a potential advantage in bridge vibration energy harvesting and providing power for self-powered sensors.

Dynamics of a model for the degradation mechanism of aggregated α-synuclein in Parkinson's disease.

Accumulation of the misfolded synaptic protein α-synuclein (αSyn*) is a hallmark of neurodegenerative disease in Parkinson's disease (PD). Recent studies suggest that the autophagy lysosome pathway (ALP) including both the Beclin1-associated and mTOR-signaling pathways is involved in the αSyn* clearance mechanism. In this study, a mathematical model is proposed for the degradation of αSyn* by ALP with the crosstalk element of mTOR. Using codimension-1 bifurcation analysis, the tri-stability of αSyn* is surveyed under three different stress signals and, in addition, consideration is given to the regulatory mechanisms for the Beclin1- and mTOR-dependent rates on αSyn* degradation using the codimension-1 and-2 bifurcation diagrams. It was found that, especially under internal and external oxidative stresses (S 1), the bistable switch of the aggregation of αSyn* can be transformed from an irreversible to a reversible condition through the ALP degradation pathways. Furthermore, the robustness of the tri-stable state for the stress S 1 to the parameters related to mTOR-mediated ALP was probed. It was confirmed that mTOR-mediated ALP is important for maintaining the essential dynamic features of the tri-stable state. This study may provide a promising avenue for conducting further experiments and simulations of the degradation mechanism of dynamic modeling in PD.

Positive role of bifurcation on stochastic resonance and its application in fault diagnosis under time-varying rotational speed

Stochastic resonance (SR) is mainly produced by the synergistic effect of noise, nonlinear system, and signals. This converts a part of the noise energy into useful signal energy, thereby improving the output of the system. When rotating machinery starts and stops, driving force and load will cause the variation of speed, and thus the produced vibration signal has strong non-stationary characteristics. Furthermore, although SR can be used to process non-stationary signals, its system parameters need to be matched in real-time, and therefore its application and development are limited. This paper mainly studies an adaptive frequency-shift SR of the tri-stable nonlinear system. On the one hand, order analysis can transform non-stationary signals into stationary signals, which shows the advantages of SR in stationary signal processing. On the other hand, the change of system parameters switches the system from tri-stable state to bistable and monostable state, so it loses the advantage of tri-stable weak signal detection. The variation of potential well depth, bifurcation phenomenon, and steady-state switching process caused by system parameters are studied, to help facilitate the control of the system parameters to determine the steady-state situation. Finally, SR is applied to the fault diagnosis of rolling bearing under variable speed conditions and the background of strong noise, which effectively extracts weak fault features.

The role of harvesting in population control in the presence of correlated noise sources

In this paper, we compare the role of constant and Michaelis-Menten type harvesting in single species population control in presence of correlated noise sources. Our aim is to determine a statistical correlation between the noises in the model parameters and population size. The characteristic time scale over which the population size of prey and predator varies are very much different, this fact justifies to consider a single species model as the predator population can be chosen to be constant within the generation time of prey. Steady state probability distributions and stationary potentials of the population are determined by Fokker-Planck equations. Stochastic bifurcation analysis and mean first passage times have been computed. Noise induced critical transitions are observed depending on the strength of the noises. The extinction possibility of population in stochastic control with Michaelis-Menten type harvesting is higher than the constant harvesting. One of our key findings is the transition from bistable to tristable state for weak noises. Another valuable finding is the noise enhanced stability phenomenon for negatively correlated noises. Constant rate of harvesting is better in deterministic case whereas Michaelis-Menten type harvesting is better in stochastic case to reduce population size. The obtained results may be helpful to understand toxin producing phytoplankton blooms and its control in marine ecosystem. Moreover, the study can be useful to explain wild prey population outbreak or extinction in forest.

Time-Domain Dynamic Characteristics Analysis and Experimental Research of Tri-Stable Piezoelectric Energy Harvester.

In order to explore the dynamic characteristics of the linear-arch beam tri-stable piezoelectric energy harvester (TPEH), a magnetic force model was established by the magnetic dipole method, and the linear-arch composite beam nonlinear restoring force model was obtained through experiments. Based on the Euler–Bernoulli beam theory, a system dynamic model is established, and the influence of the horizontal distance, vertical distance and excitation acceleration of magnets on the dynamic characteristics of the system is simulated and analyzed. Moreover, the correctness of the theoretical results is verified by experiments. The results show that the system can be mono-stable, bi-stable and tri-stable by adjusting the horizontal or vertical spacing of the magnets under proper excitation. The potential well of the system in the tri-stable state is shallow, and it is easier to achieve a large-amplitude response. Increasing the excitation level is beneficial for the large-amplitude response of the system. This study provides theoretical guidance for the design of linear-arch beam TPEH.

Performance of a novel dual-magnet tri-stable piezoelectric energy harvester subjected to random excitation

Usually conventional nonlinear tri-stable piezoelectric energy harvesters (TPEHs) contain two external magnets, which make both the system structure and dynamic analysis more complex. Herein, a novel dual-magnet TPEH with only one external magnet is proposed. This TPEH consists of a rectangular magnet, a piezoelectric cantilever beam, a ring magnet and a base. Next, the lumped-parameter model of the TPEH is established to obtain the dynamic equation, circuit equation, magnetic force expression and potential function. The analysis of the magnetic force expression and potential function finds that the system degenerates from a tri-stable state to a bi-stable state, and then to a mono-stable state with the increase of magnet distance due to the changes of magnetic force. Subsequently, Runge-Kutta method is used to simulate the nonlinear dynamics and energy harvesting performance of the energy harvester under the filtered Gaussian white noise over the frequency range of 0–120 Hz. Simulation results shows that the harvester changes from intra-well movement to inter-well movement with a few transitions, and then to inter-well movement with many transitions as excitation level increases. Additionally, the output performance in the bi-stable state is better than that in the tri-stable state when the excitation is small, and the output performance in the tri-stable state is better than that in the bi-stable state when the excitation is large enough. The reason is that the depth and width of the outer potential wells in the tri-stable state are deeper and narrower, while the distance between the two outer wells in the tri-stable state is larger, when compared to the bi-stable state. Finally, designed experiments are carried out to determine the parameters in the dynamic equation and measure the energy harvesting performance of the TPEH. Experimental results are consistent with simulation results. This study suggests that it is practicable to use the dual-magnet structure for constructing a multi-stable piezoelectric energy harvester.

Investigation on the energy trapping and conversion performances of a multi-stable vibration absorber

Multi-stable energy harvesters have emerged as the most attractive candidates for vibration-based energy harvesting recently. Energy trapping and energy conversion are the main characteristics of a vibration-based energy harvester, similarly, energy absorption and damping dissipation are the main features of a conventional dynamic vibration absorber (DVA). Therefore, combination of vibration absorption and energy conversion is a potential strategy for vibration control and self-powered wireless sensors. This paper presents the principle design of tri-stable systems and mathematical modeling of a 2-dof tri-stable DVA and energy harvester. The energy harvesting performances of multi-stable energy harvesters in terms of tri-stable electromagnetic energy harvester (TEEH) and bi-stable electromagnetic energy harvester (BEEH) are evaluated under impulsive excitations and harmonic vibrations, respectively. The energy trapping capacity of TEEH is calculated under single impulsive excitation and compared with its counterpart of BEEH. Furthermore, the dynamic characteristics of the multi-stable DVA (tri-stable and bi-stable) are studied. Simulation results show that TEEH induces a more rapid attenuation in the residual kinetic energy of the primary system excited by a weak impulse than its counterpart of BEEH, and the trapped energy in TEEH increases remarkably with the application of a weak impulse. Compared with BEEH, the energy dissipation and harvesting performances of TEEH are more satisfactory under low-amplitude impulse and low mass ratio conditions. Additionally, the snap-through motion can be more easily triggered in TEEH under broadband and low-amplitude vibrations. With the increase in vibration amplitude, the multi-stable mechanism of TEEH can be readily understood through observing phase portrait and Poincaré mapping, from which tri-stable state, chaotic attractors and bi-stable state are presented successively. Moreover, the energy harvesting efficiency of TEEH is more advanced under broadband ambient vibrations in comparison with BEEH. Finally, a prototype of tunable tri-stable system composed of a linear spring and magnetic spring is proposed.

An adaptive vibrational resonance method based on cascaded varying stable-state nonlinear systems and its application in rotating machine fault detection

A weak character signal with low frequency can be detected based on the mechanism of vibrational resonance (VR). The detection performance of VR is determined by the synergy of a weak low-frequency input signal, an injected high-frequency sinusoidal interference and the nonlinear system(s). In engineering applications, there are many weak fault signals with high character frequencies. These fault signals are usually submerged in strong background noise. To detect these weak signals, an adaptive detection method for a weak high-frequency fault signal is proposed in this paper. This method is based on the mechanics of VR and cascaded varying stable-state nonlinear systems (VSSNSs). Partial background noise with high frequency is regarded as a special type of high-frequency interference and an energy source that protrudes a weak fault signal. In this way, high-frequency background noise is utilized in a VSSNS. To improve the detection ability, manually generated high-frequency interference is injected into another VSSNS. The VSSNS can be transformed into a monostable state, bistable state or tristable state by tuning the system parameters. The proposed method is validated by a simulation signal and industrial applications. The results show the effectiveness of the proposed method to detect a weak high-frequency character signal in engineering problems.

Towards DNA-damage induced autophagy: A Boolean model of p53-induced cell fate mechanisms

How a cell determines a given phenotype upon damaged DNA is an open problem. Cell fate decisions happen at cell cycle checkpoints and it is becoming clearer that the p53 pathway is a major regulator of cell fate decisions involving apoptosis or senescence upon DNA damage, especially at G1/S. However, recent results suggest that this pathway is also involved in autophagy induction upon DNA damage. To our knowledge, in this work we propose the first model of the DNA damage-induced G1/S checkpoint contemplating the decision between three phenotypes: apoptosis, senescence, and autophagy. The Boolean model is proposed based on experiments with U87 glioblastoma cells using the transfection of miR-16 that can induce a DNA damage response. The wild-type case of the model shows that DNA damage induces the checkpoint and the coexistence of the three phenotypes (tristable dynamics), each with a different probability. We also predict that the positive feedback involving ATM, miR-16, and Wip1 has an influence on the tristable state. The model predictions were compared to experiments of gain and loss of function in other three different cell lines (MCF-7, A549, and U2OS) presenting agreement. For p53-deficient cell lines such as HeLa, H1299, and PC-3, our model contemplates the experimental observation that the alternative AMPK pathway can compensate this deficiency. We conclude that at the G1/S checkpoint the p53 pathway (or, in its absence, the AMPK pathway) can regulate the induction of different phenotypes in a stochastic manner in the U87 cell line and others.

Logic Gate Functions Built with Nonvolatile Resistive Switching and Thermoresponsive Memory Based on Biologic Proteins.

Logic gate functions built with nonvolatile resistive switching and thermoresponsive memory based on biologic proteins were investigated. The "NAND" and "NOR" functions of logic gates in soya protein devices have been built at room temperature by their nonvolatile ternary WORM resistive switching behaviors. Furthermore, heating the devices from room temperature to 358 K results in a switch from tristable state to bistable state WORM resistive switching behavior, indicating that the thermoresponsiveness can be efficiently memorized. The biologic transient nonvolatile memory device consisting of soya protein is illustrated. This device exhibits a long data retention time (104 s) and significant HRS/LRS ratio (∼105); the transient response of the current to voltage of an as-fabricated device is also explored. The soya protein based memory device on a gelatin film substrate is also assessed to validate the feasibility of degradation and biological compatibility for the implantable biological electronic device, that is, innoxious and avirulent to the human body. This can offer alternative avenues for exploring prospective bioelectronic devices.

Mean-field dispersal induced synchrony and stability in an epidemic model under patchy environment

In our highly connected modern world, the dispersion of population is very important at the time when disease spread to evaluate its nature i.e., whether the disease will die-out or grow. Therefore, in this paper, SIR (Susceptible–Infected–Recovered) model is framed to describe the dispersal of population for different patches (communities) which are interconnected using mean field diffusive coupling. The effect of coupling on the dynamics of the epidemiology classes among different patches has been investigated. The dynamics of the epidemiology classes is explored under the environment of symmetric coupling and asymmetric coupling. It is shown that the synchronization and stability of Disease Free Equilibrium (or Endemic Equilibrium) can be attained simultaneously through the mechanism of suppression of oscillations namely amplitude death (AD) and oscillation death (OD). Irrespective of coupling environment i.e., symmetric and asymmetric, we have observed the tri-stable state and its transition from different states through Hopf bifurcation and transcritical bifurcation. The basic reproduction number is also established for the stability of Disease Free Equilibrium and Endemic Equilibrium. Through bifurcation analysis, it has been found that the disease can become stable or it can die out through dispersal of population among patches.

Humans Perceive Binocular Rivalry and Fusion in a Tristable Dynamic State

Human vision combines inputs from the two eyes into one percept. Small differences "fuse" together, whereas larger differences are seen "rivalrously" from one eye at a time. These outcomes are typically treated as mutually exclusive processes, with paradigms targeting one or the other and fusion being unreported in most rivalry studies. Is fusion truly a default, stable state that only breaks into rivalry for non-fusible stimuli? Or are monocular and fused percepts three sub-states of one dynamical system? To determine whether fusion and rivalry are separate processes, we measured human perception of Gabor patches with a range of interocular orientation disparities. Observers (10 female, 5 male) reported rivalrous, fused, and uncertain percepts over time. We found a dynamic "tristable" zone spanning from ∼25-35° of orientation disparity where fused, left-eye-, or right-eye-dominant percepts could all occur. The temporal characteristics of fusion and non-fusion periods during tristability matched other bistable processes. We tested statistical models with fusion as a higher-level bistable process alternating with rivalry against our findings. None of these fit our data, but a simple bistable model extended to have three states reproduced many of our observations. We conclude that rivalry and fusion are multistable substates capable of direct competition, rather than separate bistable processes.SIGNIFICANCE STATEMENT When inputs to the two eyes differ, they can either fuse together or engage in binocular rivalry, where each eye's view is seen exclusively in turn. Visual stimuli have often been tailored to produce either fusion or rivalry, implicitly treating them as separate mutually-exclusive perceptual processes. We have found that some similar-but-different stimuli can result in both outcomes over time. Comparing various simple models with our results suggests that rivalry and fusion are not independent processes, but compete within a single multistable system. This conceptual shift is a step toward unifying fusion and rivalry, and understanding how they both contribute to the visual system's production of a unified interpretation of the conflicting images cast on the retina by real-world scenes.

A weak signal detection method based on adaptive parameter-induced tri-stable stochastic resonance

Aiming at detecting the weak signal in a strong noise background, an enhanced weak signal detection method based on adaptive parameter-induced tri-stable stochastic resonance is proposed. Firstly, because the system can switch among the monostable, bistable and tri-stable state, the potential function characteristic of tri-stable systems is studied by analyzing the potential function curves with different system parameters. And the dynamic characteristics of system parameters on the depth of the potential well is analyzed. The ranges of R and the system parameters are determined, which is essential for ensuring the system is tri-stable state. Secondly, the range of R is used as the constraint condition and the average output signal-to-noise ratio is used as the fitness function of the adaptive algorithm. The system parameters a, b, c are optimized by the differential evolution particle swarm optimization (DEPSO) method to obtain the best output effect. Finally, the proposed adaptive parameter-induced tri-stable stochastic resonance method is adopted to detect the mixed multiple high-frequency weak signal. The detection results are compared with that of adaptive bistable stochastic resonance. At the meanwhile, the method is also applied to detect the fault signal of single crystal furnace. Both the simulation analysis and experiment results show that the proposed method can effectively improve the output signal-to-noise ratio and detect multi-frequency weak signal in the strong noise background.

Photo-manipulated photonic bandgap devices based on optically tristable chiral-tilted homeotropic nematic liquid crystal.

We report on the spectral properties of an optically switchable tristable chiral-tilted homeotropic nematic liquid crystal (LC) incorporated as a tunable defect layer in one-dimensional photonic crystal. By varying the polarization angle of the incident light and modulating the light intensity ratio between UV and green light, various transmission characteristics of the composite were obtained. The hybrid structure realizes photo-tunability in transmission of defect-mode peaks within the photonic bandgap in addition to optical switchability among three distinct sets of defect modes via photoinduced tristable state transitions. Because the fabrication process is easier and less critical in terms of cell parameters or sample preparation conditions and the LC layer itself possesses an extra stable state compared with the previously reported bistable counterpart operating on the basis of biased-voltage dual-frequency switching, it has much superior potential for photonic applications such as a low-power-consumption multichannel filter and an optically controllable intensity modulator.

Dynamic and energetic characteristics of a tri-stable magnetopiezoelastic energy harvester

In this study, a mathematical model of a tri-stable energy harvester is developed and used to investigate its formation mechanisms for multi-stability states, nonlinear dynamic behaviors, and power generation performance. Bifurcation analyses for the equilibrium solution of the derived model system are performed. It is shown that the present energy harvester system can exhibit multi-stable (mono-, bi-, and tri-stable) behaviors depending on the two geometric parameters associated with the locations of the tip and external magnets. It is also found that the tri-stability is initiated by a new pitchfork bifurcation or a degenerate pitchfork bifurcation that leads to a pair of saddle-node bifurcations. Bifurcation set diagram is obtained in the parametric space of these two geometric parameters, which can be used to design the potential wells of the multi-stable energy harvesters. Potential energy diagrams are also obtained and they show that the distance between the outer potential energy wells for the tri-stable state is formed in a way that it is larger than that for the equivalent bi-stable state. A series of numerical simulations performed on the present system well illustrates the high output power generation characteristics of the tri-stable energy harvester over a broad operating frequency band.

Electric field tuning of non-volatile three-state magnetoelectric memory in FeCo-NiFe2O4/Pb(Mg1/3Nb2/3)0.7Ti0.3O3 heterostructures

We demonstrate electric field impulse-induced reversible tristable magnetization switching in FeCo-NiFe2O4/Pb(Mg1/3Nb2/3)0.7Ti0.3O3 (PMN-PT) heterostructures at room temperature. The magnetic properties of the FeCo-NiFe2O4 film can be changed reversibly by the strain-mediated magnetoelectric coupling effect. Three piezostrain-mediated reversible and stable electric resistance states were obtained in the FeCo-NiFe2O4 film when different electric field impulses were applied, including large positive and negative fields and an impulse that was smaller than the electric coercive field. Consequently, reversible electric field impulse tuning of the tristable resistance state, which is related to the different magnetization switching properties of the materials, was realized. These results provide a promising approach for low loss multistate magnetoelectric memory devices for information storage applications.

Synthesis and characterization of achiral banana‐shaped liquid crystalline molecules containing bisnaphthyl moieties

Three analogous series of symmetric banana‐shaped liquid crystalline molecules containing bisnaphthyl units were synthesized and characterized. The effects of linking groups (on the side wings) and lateral meta‐fluoro substitutions (on the middle outer rings) on the mesogenic properties were examined. The type of mesophase depends on the lengths of terminal alkoxy chains. Thus, achiral molecules with shorter flexible chains (n = 8) exhibit a rectangular columnar (B1) phase, while analogous derivatives with longer flexible chains (n = 12) display the B2 phase. All lateral meta‐fluoro substituted analogues (series II) possess the lowest isotropization temperatures and the narrowest mesophasic ranges of the B1 and B2 phases. The B1 and B2 phases were confirmed by X‐ray diffraction, polarizing optical microscopy (POM) and electro‐optical (EO) switching experiments. An electric field‐induced transition from an antiferroelectric (tristable) state to a ferroelectric (bistable) state was observed in the EO measurements. Spontaneous polarization (by switching current response), tilt angle of chiral domains (by POM), and transmittance–voltage measurements of the B2 phase in related compounds have been surveyed in this study.