Bistable Dynamics Research Articles

Timescale separation and models of symbiosis: state space reduction, multiple attractors and initialization.

Dynamic Energy Budget models relate whole organism processes such as growth, reproduction and mortality to suborganismal metabolic processes. Much of their potential derives from extensions of the formalism to describe the exchange of metabolic products between organisms or organs within a single organism, for example the mutualism between corals and their symbionts. Without model simplification, such models are at risk of becoming parameter-rich and hence impractical. One natural simplification is to assume that some metabolic processes act on ‘fast’ timescales relative to others. A common strategy for formulating such models is to assume that ‘fast’ processes equilibrate immediately, while ‘slow’ processes are described by ordinary differential equations. This strategy can bring a subtlety with it. What if there are multiple, interdependent fast processes that have multiple equilibria, so that additional information is needed to unambiguously specify the model dynamics? This situation can easily arise in contexts where an organism or community can persist in a ‘healthy’ or an ‘unhealthy’ state with abrupt transitions between states possible. To approach this issue, we offer the following: (a) a method to unambiguously complete implicitly defined models by adding hypothetical ‘fast’ state variables; (b) an approach for minimizing the number of additional state variables in such models, which can simplify the numerical analysis and give insights into the model dynamics; and (c) some implications of the new approach that are of practical importance for model dynamics, e.g. on the bistability of flux dynamics and the effect of different initialization choices on model outcomes. To demonstrate those principles, we use a simplified model for root-shoot dynamics of plants and a related model for the interactions between corals and endosymbiotic algae that describes coral bleaching and recovery.

Hybridizing piezoelectric and electromagnetic mechanisms with dynamic bistability for enhancing low-frequency rotational energy harvesting

This Letter proposes a rotational energy harvester with hybrid piezoelectric and electromagnetic mechanisms and dynamic bistability. It consists of a piezoelectric stack with a force magnification frame and two connected springs, and two electromagnetic coils with inner impact stoppers. On the one hand, the hybrid energy transduction is applied in the gravity-based rotational energy harvester to enhance the energy output. On the other hand, the dynamic bistability by utilizing the centrifugal force is proposed to improve low-frequency performances. Simulation and experiments demonstrate that the proposed harvester starts to exhibit the bistability as the rotational frequency is increased from zero with subsequent interwell, chaotic, and intrawell motions, among which the interwell motions can increase the peak power from piezoelectric and electromagnetic parts by 24.99% and 57.41%, respectively. Specifically, the maximum total output power in experiments is measured to be 2.98 mW at 7.5 Hz and the spring stiffness of 4200 N/m. Moreover, the total power and frequency bandwidth are both higher but broader/narrower with a higher spring stiffness or impact distance, respectively.

Short Pyridine-Furan Springs Exhibit Bistable Dynamics of Duffing Oscillators.

The intensive development of nanodevices acting as two-state systems has motivated the search for nanoscale molecular structures whose dynamics are similar to those of bistable mechanical systems, such as Euler arches and Duffing oscillators. Of particular interest are the molecular structures capable of spontaneous vibrations and stochastic resonance. Recently, oligomeric molecules that were a few nanometers in size and exhibited the bistable dynamics of an Euler arch were identified through molecular dynamics simulations of short fragments of thermo-responsive polymers subject to force loading. In this article, we present molecular dynamics simulations of short pyridine-furan springs a few nanometers in size and demonstrate the bistable dynamics of a Duffing oscillator with thermally-activated spontaneous vibrations and stochastic resonance.

Desolvation–Solvation-Induced Reversible On–Off Switching of Two Memory Channels in a Cobalt(II) Coordination Polymer: Overlay of Spin Crossover and Structural Phase Transition

Desolvation–Solvation-Induced Reversible On–Off Switching of Two Memory Channels in a Cobalt(II) Coordination Polymer: Overlay of Spin Crossover and Structural Phase Transition

M-center in 4H-SiC: Isothermal DLTS and first principles modeling studies

We report on a bistable defect known as M-center, here introduced in n-type 4H-SiC by 2 MeV He ion implantation. Deep levels of the M-center are investigated by means of junction spectroscopy techniques, namely, deep level transient spectroscopy (DLTS) and isothermal DLTS. In addition to previously reported three deep levels arising from the M-center (labeled as M1, M2, and M3), we provide direct evidence on the existence of a fourth transition (labeled as M4) with an activation energy of 0.86 eV. Activation energies and apparent capture cross sections for all four metastable defects are determined. From first-principles calculations, it is shown that the observed features of the M-center, including the charge state character, transition levels, bi-stability dynamics, and annealing, are all accounted for by a carbon self-interstitial.

An interplay of soil salinization and groundwater degradation threatening coexistence of oasis-desert ecosystems

In salt-affected and groundwater-fed oasis-desert systems, water and salt balance is critically important for stable coexistence of oasis-desert ecosystems, especially in the context of anthropogenic-induced over-development and perturbations due to climate variability that affects the sustainability of human-natural systems. Here, an investigation of the spatio-temporal variability of soil salinity and groundwater dynamics across four different hydrological regions in oasis-desert system is performed. An evaluation of the effects of soil salinization and groundwater degradation interplays on the coexistence of oasis-desert ecosystems in northwestern China is undertaken over 1995–2020, utilizing comprehensive measurements and ecohydrological modelling framework. We note that the process of salt migration and accumulation across different landscapes in oasis-desert system is reshaping, with soil salinization accelerating especially in water-saving agricultural irrigated lands. The continuous decline in groundwater tables, dramatic shifts in groundwater flow patterns and significant degradation of groundwater quality are occurring throughout the watershed. Worse so, a clear temporal-spatial relationship between soil salinization and groundwater degradation appearing to exacerbate the regional water-salt imbalance. Also, the eco-environmental flows are reaching to their limit with watershed closures, although these progressions were largely hidden by regional precipitation and streamflow variability. The oasis-desert ecosystems tend to display bistable dynamics with two preferential configurations of bare and vegetated soils, and soil salinization and groundwater degradation interplays are causing catastrophic shift in the oasis-desert ecosystems. The results highlight the importance of regional adaptive water and salt management to maintain the coexistence of oasis-desert ecosystems in arid areas.

Discrete dynamical models on Wolbachia infection frequency in mosquito populations with biased release ratios

We develop two discrete models to study how supplemental releases affect the Wolbachia spreading dynamics in cage mosquito populations. The first model focuses on the case when only infected males are released at each generation. This release strategy has been proved to be capable of speeding up the Wolbachia persistence by suppressing the compatible matings between uninfected individuals. The second model targets the case when only infected females are released at each generation. For both models, detailed model formulation, enumeration of the positive equilibria and their stability analysis are provided. Theoretical results show that the two models can generate bistable dynamics when there are three positive equilibrium points, semi-stable dynamics for the case of two positive equilibrium points. And when the positive equilibrium point is unique, it is globally asymptotically stable. Some numerical simulations are offered to get helpful implications on the design of the release strategy.

Nonlinear Localization of Dissipative Modulation Instability

Modulation instability (MI) in the presence of noise typically leads to an irreversible and complete disintegration of a plane wave background. Here we report on experiments performed in a coherently driven nonlinear optical resonator that demonstrate nonlinear localization of dissipative MI: formation of persisting domains of MI-driven spatiotemporal chaos surrounded by a stable quasi-plane-wave background. The persisting localization ensues from a combination of bistability and complex spatiotemporal nonlinear dynamics that together permit a locally induced domain of MI to be pinned by a shallow modulation on the plane wave background. We further show that the localized domains of spatiotemporal chaos can be individually addressed-turned on and off at will-and we explore their transport behavior as the strength of the pinning is controlled. Our results reveal new fundamental dynamics at the interface of front dynamics and MI, and offer a route for tailored patterns of noiselike bursts of light.

Incoherent modulation of bi-stable dynamics orchestrates the Mushroom and Isola bifurcations

In biological networks, steady state dynamics of cell-fate regulatory genes often exhibit Mushroom and Isola kind of bifurcations. How these complex bifurcations emerge for these complex networks, and what are the minimal network structures that can generate these bifurcations, remain elusive. Herein, by employing Waddington’s landscape theory and bifurcation analysis, we demonstrate that Mushroom and Isola bifurcations can be realized with four minimal network motifs that are constituted by combining a positive feedback motif with various incoherent feed-forward loops. Our study reveals that the intrinsic bi-stable dynamics originating from the positive feedback motif can be fine-tuned by altering the extent of the incoherence of these minimal networks to produce these complex bifurcations. These modeling insights will be useful in identifying the possible network motifs that may give rise to either Mushroom or Isola bifurcation in other biological systems.

A Shearless Microfluidic Device Detects a Role in Mechanosensitivity for AWCON Neuron in Caenorhabditis elegans.

AWC olfactory neurons are fundamental for chemotaxis toward volatile attractants in Caenorhabditis elegans. Here, it is shown that AWCON responds not only to chemicals but also to mechanical stimuli caused by fluid flow changes in a microfluidic device. The dynamics of calcium events are correlated with the stimulus amplitude. It is further shown that the mechanosensitivity of AWCON neurons has an intrinsic nature rather than a synaptic origin, and the calcium transient response is mediated by TAX-4 cGMP-gated cation channel, suggesting the involvement of one or more "odorant" receptors in AWCON mechano-transduction. In many cases, the responses show plateau properties resembling bistable calcium dynamics where neurons can switch from one stable state to the other. To investigate the unprecedentedly observed mechanosensitivity of AWCON neurons, a novel microfluidic device is designed to minimize the fluid shear flow in the arena hosting the nematodes. Animals in this device show reduced neuronal activation of AWCON neurons. The results observed indicate that the tangential component of the mechanical stress is the main contributor to the mechanosensitivity of AWCON . Furthermore, the microfluidic platform, integrating shearless perfusion and calcium imaging, provides a novel and more controlled solution for in vivo analysis both in micro-organisms and cultured cells.

Noise-induced properties of active dendrites

Dendrites play an essential role in the integration of highly fluctuating input in vivo into neurons across all nervous systems. Yet, they are often studied under conditions where inputs to dendrites are sparse. The dynamic properties of active dendrites facing in vivo-like fluctuating input thus remain elusive. In this paper, we uncover dynamics in a canonical model of a dendritic compartment with active calcium channels, receiving in vivo-like fluctuating input. In a single-compartment model of the active dendrite with fast calcium activation, we show noise-induced nonmonotonic behavior in the relationship of the membrane potential output, and mean input emerges. In contrast, noise can induce bistability in the input-output relation in the system with slowly activating calcium channels. Both phenomena are absent in a noiseless condition. Furthermore, we show that timescales of the emerging stochastic bistable dynamics extend far beyond a deterministic system due to stochastic switching between the solutions. A numerical simulation of a multicompartment model neuron shows that in the presence of in vivo-like synaptic input, the bistability uncovered in our analysis persists. Our results reveal that realistic synaptic input contributes to sustained dendritic nonlinearities, and synaptic noise is a significant component of dendritic input integration.

Dynamics of a stage-structured predator-prey model: cost and benefit of fear-induced group defense

In the predator-prey system, predators can affect the prey population (1) by direct killing and (2) by inducing predation fear, which ultimately force preys to adopt some anti-predator strategies. However, the anti-predator strategy is not the same for all individual preys of different life stages. Also, anti-predator behavior has both cost and benefit, but most of the mathematical models observed the dynamics by incorporating its cost only. In the present study, we formulate a predator-prey model dividing the prey population into two stages: juvenile and adult. We assume that adult preys are only adapting group defense as an anti-predator strategy when they are sensitive to predation. Group defense plays a positive role for adult prey by reducing their predation, but, on the negative side, it simultaneously decreases their reproductive potential. A parameter, anti-predator sensitivity is introduced to interlink both the benefit and cost of group defense. Our result shows that when adult preys are not showing anti-predator behavior, with an increase of maturation rate, the system exhibits a population cycle of abruptly increasing amplitude, which may drive all species of the system to extinction. Anti-predator sensitivity may exclude oscillation through homoclinic bifurcation and avert the prey population for any possible random extinction. Anti-predator sensitivity also decreases the predator population density and produces bistable dynamics. Higher values of anti-predator sensitivity may lead to the extinction of the predator population and benefit adult preys to persist with large population density. Below a threshold value of anti-predator sensitivity, it may possible to retain the predator population in the system by increasing the fear level of the predator. We also observe our fear-induced stage-structured model exhibits interesting and rich dynamical behaviors, various types of bistabilities in different bi-parameter planes. Finally, we discuss the potential impact of our findings.

Experimental study and passive control of the bistable dynamics of the three-dimensional air-wake flow of a finite-width double backward-facing step

Inspired by the study of Rao et al. (2019), the aerodynamics of a simplified frigate is investigated experimentally. The natural wake flow dynamics is shown to be bi-stable at zero yaw angles, at both the rear of the ship superstructure and the stern. The bi-stable dynamics is strongly weakened at the stern when the ship is lifted off the ground in the free-stream. Perimetric cavities of sufficient depth at the rear of the superstructure are able to suppress the bi-stable dynamics and to symmetrize the air-wake flow at both the superstructure and the stern. The base pressure increases with the cavity depth while the drag force slightly decreases. Our study experimentally confirms that perimetric rear cavities offer efficient devices for passive flow control strategies of the aerodynamic air-wake flow of bodies of complex geometries subject to bi-stable dynamics.

Dynamics of the Auditory Continuity Illusion.

Illusions give intriguing insights into perceptual and neural dynamics. In the auditory continuity illusion, two brief tones separated by a silent gap may be heard as one continuous tone if a noise burst with appropriate characteristics fills the gap. This illusion probes the conditions under which listeners link related sounds across time and maintain perceptual continuity in the face of sudden changes in sound mixtures. Conceptual explanations of this illusion have been proposed, but its neural basis is still being investigated. In this work we provide a dynamical systems framework, grounded in principles of neural dynamics, to explain the continuity illusion. We construct an idealized firing rate model of a neural population and analyze the conditions under which firing rate responses persist during the interruption between the two tones. First, we show that sustained inputs and hysteresis dynamics (a mismatch between tone levels needed to activate and inactivate the population) can produce continuous responses. Second, we show that transient inputs and bistable dynamics (coexistence of two stable firing rate levels) can also produce continuous responses. Finally, we combine these input types together to obtain neural dynamics consistent with two requirements for the continuity illusion as articulated in a well-known theory of auditory scene analysis: responses persist through the noise-filled gap if noise provides sufficient evidence that the tone continues and if there is no evidence of discontinuities between the tones and noise. By grounding these notions in a quantitative model that incorporates elements of neural circuits (recurrent excitation, and mutual inhibition, specifically), we identify plausible mechanisms for the continuity illusion. Our findings can help guide future studies of neural correlates of this illusion and inform development of more biophysically-based models of the auditory continuity illusion.

Improved bistable mechanism for wave energy harvesting

As one of the renewable and clean energy sources, wave energy has high density and all-day availability characteristics. However, the development of wave energy converters has been hampered, mainly because of the low efficiency induced high levelized energy costs. The present study introduces an improved bistable mechanism composed of three linear springs, aiming to enhance the performance of a point absorber employed as a wave energy converter. The improved bistable mechanism features an asymmetric configuration of three linear stiffness springs: one horizontal and two obliques on a vertical plane. Numerical simulations based on Cummins equations in the time domain describe the point absorber dynamic behavior in regular and irregular waves. The improved bistable wave energy converter featured a wider low equivalent stiffness range than linear and conventional bistable counterparts, improving its ability to frequency shifting. Its lower potential barrier greatly improves the capture width ratio and frequency bandwidth at low excitations. Such characteristics facilitate the improved bistable wave energy converter to achieve higher efficiency than its linear and conventional bistable counterparts at low frequencies, and enhance its robustness against power-take-off damping detuning and sea state changes. These features altogether make the improved bistable mechanism an efficient alternative to explore the benefits of the bistable dynamics applied to wave energy converters.

Global analysis of a juvenile-adult model for cannibalistic species

Cannibalism is a life trait occurring in a wide variety of species. To describe the population dynamics of cannibalistic species, we develop a stage-structured population model in which adults prey on juveniles with a Holling type I functional response. We make a rigorous analysis of the global dynamics in the model. The results of theoretical analysis show that the model has no boundary equilibrium other than the extinction one since juveniles and adults are cooperative (adults reproduce juveniles and juveniles grow into adults). Under certain conditions, the model has multiple interior equilibria and exhibits several types of bistable dynamics, in which different initial densities of juveniles and adults produce different long-term outcomes.

Arrhythmogenic effects of ultra-long and bistable cardiac action potentials.

Contemporary accounts of the initiation of cardiac arrhythmias typically rely on after-depolarizations as the trigger for reentrant activity. The after-depolarizations are usually triggered by calcium entry or spontaneous release within the cells of the myocardium or the conduction system. Here we propose an alternative mechanism whereby arrhythmias are triggered autonomously by cardiac cells that fail to repolarize after a normal heartbeat. We investigated the proposal by representing the heart as an excitable medium of FitzHugh-Nagumo cells where a proportion of cells were capable of remaining depolarized indefinitely. As such, those cells exhibit bistable membrane dynamics. We found that heterogeneous media can tolerate a surprisingly large number of bistable cells and still support normal rhythmic activity. Yet there is a critical limit beyond which the medium is persistently arrhythmogenic. Numerical analysis revealed that the critical threshold for arrhythmogenesis depends on both the strength of the coupling between cells and the extent to which the abnormal cells resist repolarization. Moreover, arrhythmogenesis was found to emerge preferentially at tissue boundaries where cells naturally have fewer neighbors to influence their behavior. These findings may explain why atrial fibrillation typically originates from tissue boundaries such as the cuff of the pulmonary vein.

Controlled bistable dynamics of a four-mirror cavity-optomechanics with two movable mirrors

We investigate the controlled bistable dynamics in a four-mirror optomechanical cavity with two transversely located macroscopic movable mirrors. A strong external pump laser longitudinally drives the cavity, building up a strong cavity mode which interacts with the movable mirrors after getting split from beam splitter. Two mechanical drives externally interact with each of the movable mirrors perturbing their oscillatory motion. We show that the bistable behavior of intra-cavity steady-state photon number, occurring because of the cavity–mirrors coupling, gets significantly enhanced with presence of external mechanical drives. These enhancements can be controlled with the strength of mechanical drive, providing an opportunity to perform optical switching at higher photon number states. Further, we illustrate that the bistable dynamics of movable mirrors are not only being controlled with external mechanical drives, but the increase in mechanical drive of one mirror also suppresses the bistability of other movable mirror with constant (or zero) mechanical drive. We also show the impacts of external mechanical drives on the effective potential of the system.

Stress granules display bistable dynamics modulated by Cdk.

Stress granules (SGs) are conserved biomolecular condensates that originate in response to many stress conditions. These membraneless organelles contain nontranslating mRNAs and a diverse subproteome, but our knowledge of their regulation and functional relevance is still incipient. Here, we describe a mutual-inhibition interplay between SGs and Cdc28, the budding yeast Cdk. Among Cdc28 interactors acting as negative modulators of Start, we have identified Whi8, an RNA-binding protein that localizes to SGs and recruits the mRNA of CLN3, the most upstream G1 cyclin, for efficient translation inhibition and Cdk inactivation under stress. However, Whi8 also contributes to recruiting Cdc28 to SGs, where it acts to promote their dissolution. As predicted by a mutual-inhibition framework, the SG constitutes a bistable system that is modulated by Cdk. Since mammalian cells display a homologous mechanism, we propose that the opposing functions of specific mRNA-binding proteins and Cdk's subjugate SG dynamics to a conserved hysteretic switch.

Bistable Bacterial Growth Dynamics in the Presence of Antimicrobial Agents.

The outcome of an antibiotic treatment on the growth capacity of bacteria is largely dependent on the initial population size (Inoculum Effect). We characterized and built a model of this effect in E. coli cultures using a large variety of antimicrobials, including conventional antibiotics, and for the first time, cationic antimicrobial peptides (CAMPs). Our results show that all classes of antimicrobial drugs induce an inoculum effect, which, as we explain, implies that the dynamic is bistable: For a range of anti-microbial densities, a very small inoculum decays whereas a larger inoculum grows, and the threshold inoculum depends on the drug concentration. We characterized three distinct classes of drug-induced bistable growth dynamics and demonstrate that in rich medium, CAMPs correspond to the simplest class, bacteriostatic antibiotics to the second class, and all other traditional antibiotics to the third, more complex class. These findings provide a unifying universal framework for describing the dynamics of the inoculum effect induced by antimicrobials with inherently different killing mechanisms.