Bistable Region Research Articles

Finite‐Element Analysis of an Antagonistic Bistable Shape Memory Alloy Beam Actuator

A finite‐element (FE) analysis of the active bistability of an antagonistic shape memory alloy (SMA) beam actuator of TiNiCu is presented. The actuator comprises two coupled SMA beams that are clamped at both ends and coupled in their center by a spacer having different memory shapes being deflected in opposite out‐of‐plane directions. The actuator is characterized by two equilibrium positions. To determine bistable behavior as a function of geometrical parameters, a force criterion is defined by the coupling force of the beams in austenitic and martensitic states. Bistable behavior is achieved, if the coupling force does not change sign in the entire displacement range. This implies that the austenitic beam dominates the opposing martensitic beam. Thus, selective heating of the SMA beams results in a snap‐through motion of the coupled SMA beams. Depending on which of the two beams is in austenitic state, either of the two equilibrium positions is reached without the need for an external force. It is demonstrated that geometrical parameters like initial predeflection and spacer length have a crucial effect on the bistable performance. Bistable regions as well as critical limits characterized by geometry‐dependent stability ratios, beyond which the actuator's performance becomes monostable, are identified.

Dynamics of a falling plate at low Reynolds numbers

Free-falling of objects in fluids is universal in nature and engineering. The falling styles of the falling object are affected by the properties of both the object and the fluid. Based on the assumption that the final state of a free-falling object at low Reynolds numbers is stable and equivalent to that of a fixed object with incoming flow, we utilize the results for the fixed plate to interpolate and obtain the state of the falling plate. It is found that the plate would exhibit multiple stable falling solutions. The number of stable falling solutions is dependent on the location of the gravity center of the plate. The distribution of the multi-solution region is affected by both Archimedes number (Ar) and the density ratio (m*). The results of the actual fall of the plate do not always agree with those obtained by the static interpolation method due to the fact that the fall of the plate is a dynamic process. We simulate the falling behaviors of plates whose center of gravity is located in the multi-solution region for different initial release angles θ0. According to the falling behaviors of the plate, there are four regions that are observed and denoted in the multi-solution region: (1) single stable region; (2) bistable region; (3) single stable and fluttering region; and (4) bistable and fluttering region. The effects of Ar,m*, and the dimensionless moment of inertia I* of the plate on the distribution of the four regions are evaluated.

The Na+/K+-ATPase generically enables deterministic bursting in class I neurons by shearing the spike-onset bifurcation structure.

Slow brain rhythms, for example during slow-wave sleep or pathological conditions like seizures and spreading depolarization, can be accompanied by oscillations in extracellular potassium concentration. Such slow brain rhythms typically have a lower frequency than tonic action-potential firing. They are assumed to arise from network-level mechanisms, involving synaptic interactions and delays, or from intrinsically bursting neurons. Neuronal burst generation is commonly attributed to ion channels with slow kinetics. Here, we explore an alternative mechanism generically available to all neurons with class I excitability. It is based on the interplay of fast-spiking voltage dynamics with a one-dimensional slow dynamics of the extracellular potassium concentration, mediated by the activity of the Na+/K+-ATPase. We use bifurcation analysis of the complete system as well as the slow-fast method to reveal that this coupling suffices to generate a hysteresis loop organized around a bistable region that emerges from a saddle-node loop bifurcation-a common feature of class I excitable neurons. Depending on the strength of the Na+/K+-ATPase, bursts are generated from pump-induced shearing the bifurcation structure, spiking is tonic, or cells are silenced via depolarization block. We suggest that transitions between these dynamics can result from disturbances in extracellular potassium regulation, such as glial malfunction or hypoxia affecting the Na+/K+-ATPase activity. The identified minimal mechanistic model outlining the sodium-potassium pump's generic contribution to burst dynamics can, therefore, contribute to a better mechanistic understanding of pathologies such as epilepsy syndromes and, potentially, inform therapeutic strategies.

The IACOB project

Context. Blue supergiants (BSGs) are key objects for understanding the evolution of massive stars, which play a crucial role in the evolution of galaxies. However, discrepancies between theoretical predictions and empirical observations have opened up important questions yet to be answered. Studying statistically significant and unbiased samples of these objects can help to improve the situation. Aims. We perform a homogeneous and comprehensive quantitative spectroscopic analysis of a large sample of Galactic luminous blue stars (a majority of which are BSGs) from the IACOB spectroscopic database, providing crucial parameters to refine and improve theoretical evolutionary models. Methods. We derived the projected rotational velocity (υ sin i) and macroturbulent broadening (υmac) using IACOB-BROAD, which combines Fourier transform and line-profile fitting techniques. We compared high-quality optical spectra with state-of-the-art simulations of massive star atmospheres computed with the FASTWIND code. This comparison allowed us to derive effective temperatures (Teff), surface gravities (log 𝑔), microturbulences (ξ), surface abundances of silicon and helium, and to assess the relevance of stellar winds through a wind-strength parameter (log Q). Results. We provide estimates and associated uncertainties of the above-mentioned quantities for the largest sample of Galactic luminous O9 to B5 stars spectroscopically analyzed to date, comprising 527 targets. We find a clear drop in the relative number of stars at Teff ≈ 21 kK, coinciding with a scarcity of fast rotating stars below that temperature. We speculate that this feature (roughly corresponding to B2 spectral type) might be roughly delineating the location of the empirical terminal-age main sequence in the mass range between 15 and 85 M⊙. By investigating the main characteristics of the υ sin i distribution of O stars and BSGs as a function of Teff, we propose that an efficient mechanism transporting angular momentum from the stellar core to the surface might be operating along the main sequence in the high-mass domain. We find correlations between ξ,υmac and the spectroscopic luminosity 𝓛 (defined as Teff4 / g). We also find that no more than 20% of the stars in our sample have atmospheres clearly enriched in helium, and suggest that the origin of this specific subsample might be in binary evolution. We do not find clear empirical evidence of an increase in the wind strength over the wind bi-stability region toward lower Teff.

Control of cascading failures using protective measures

Cascading failures, triggered by a local perturbation, can be catastrophic and cause irreparable damages in a wide area. Hence, blocking the devastating cascades is an important issue in real world networks. One of the ways to control the cascade is to use protective me‌asures, so that the agents decide to be protected against failure. Here, we consider a coevolution of the linear threshold mo‌del for the spread of cascading failures and a decision-making game based on the perceived risk of failure. Protected agents are less vulnerable to failure and in return the size of the cascade affects the agent’s decision to get insured. We find at what range of protection efficiency and cost of failure, the global cascades stop. Also we observe that in some range of protection efficiency, a bistable region emerges for the size of cascade and the prevalence of protected agents. Moreover, we show how savings or the ability of agents to repair can prevent cascades from occurring.

Self-mode-locked Ho:GdVO4 laser with optical bistability behavior

A watt-level 2061.3 nm self-mode-locked Ho:GdVO4 laser with optical bistability behavior was demonstrated. The bistable region was as wide as 1.66 W and the up-jump power at the on-threshold of 8.34 W was as high as 0.64 W. Meanwhile, the stable continuous wave self-mode-locking with self-start was achieved when the Ho:GdVO4 laser reached the on-threshold. The maximum average output power of 1.48 W was obtained at the incident pump power of 12.8 W, corresponding to the slope efficiency and optical-to-optical efficiency of 18.9 % and 11.6 %. At the maximum average output power, the pulse width of 124 ps was obtained at a pulse repetition frequency of 444 MHz. To the best of our knowledge, for the first time, a self-mode-locked laser with optical bistability behavior in the 2 µm spectral region has been reported.

Statistical analysis of bistable feature in a 1.55-[formula omitted] vertical cavity emitting laser

Optical bistability in telecom-band lasers has attracted significant attention because of its immense potential for applications in the fields of optical communications and optical computing. In this paper, we report on an experimental investigation of the statistical properties of a 1.55-μm bistable VCSEL. The VCSEL exhibits mode switching at a current of 5.41 mA and 4.15 mA when the pump continuously increases and decreases, respectively. Both of these switching exhibit a bistable region, indicating a polarization bistability induced by the gain saturation. By calculation of second-order autocorrelation functions with injection current, we identify different regions associated with the dynamics of different dominant modes. In particular, the statistical analysis reveals more properties of the bistable laser, such as the intensity fluctuations induced by different kinds of noise.

Control of seizure-like dynamics in neuronal populations with excitability adaptation related to ketogenic diet.

We consider a heterogeneous, globally coupled population of excitatory quadratic integrate-and-fire neurons with excitability adaptation due to a metabolic feedback associated with ketogenic diet, a form of therapy for epilepsy. Bifurcation analysis of a three-dimensional mean-field system derived in the framework of next-generation neural mass models allows us to explain the scenarios and suggest control strategies for the transitions between the neurophysiologically desired asynchronous states and the synchronous, seizure-like states featuring collective oscillations. We reveal two qualitatively different scenarios for the onset of synchrony. For weaker couplings, a bistability region between the lower- and the higher-activity asynchronous states unfolds from the cusp point, and the collective oscillations emerge via a supercritical Hopf bifurcation. For stronger couplings, one finds seven co-dimension two bifurcation points, including pairs of Bogdanov-Takens and generalized Hopf points, such that both lower- and higher-activity asynchronous states undergo transitions to collective oscillations, with hysteresis and jump-like behavior observed in vicinity of subcritical Hopf bifurcations. We demonstrate three control mechanisms for switching between asynchronous and synchronous states, involving parametric perturbation of the adenosine triphosphate (ATP) production rate, external stimulation currents, or pulse-like ATP shocks, and indicate a potential therapeutic advantage of hysteretic scenarios.

Weak coupling of neurons enables very high-frequency and ultra-fast oscillations through the interplay of synchronized phase shifts.

Recently, in the past decade, high-frequency oscillations (HFOs), very high-frequency oscillations (VHFOs), and ultra-fast oscillations (UFOs) were reported in epileptic patients with drug-resistant epilepsy. However, to this day, the physiological origin of these events has yet to be understood. Our study establishes a mathematical framework based on bifurcation theory for investigating the occurrence of VHFOs and UFOs in depth EEG signals of patients with focal epilepsy, focusing on the potential role of reduced connection strength between neurons in an epileptic focus. We demonstrate that synchronization of a weakly coupled network can generate very and ultra high-frequency signals detectable by nearby microelectrodes. In particular, we show that a bistability region enables the persistence of phase-shift synchronized clusters of neurons. This phenomenon is observed for different hippocampal neuron models, including Morris-Lecar, Destexhe-Paré, and an interneuron model. The mechanism seems to be robust for small coupling, and it also persists with random noise affecting the external current. Our findings suggest that weakened neuronal connections could contribute to the production of oscillations with frequencies above 1000 Hz, which could advance our understanding of epilepsy pathology and potentially improve treatment strategies. However, further exploration of various coupling types and complex network models is needed.

The correlation between independent edge and triangle degrees promote the explosive information spreading

In recent years, a novel phenomenon of explosive information spreading has been observed in the simplicial configuration model under the higher-order interactions, where a discontinuous transition exists. The model usually considers that the independent edge degree (i.e., the number of single edges attached to a node excluding those belonging to the triangles) and triangle degree (i.e., the number of triangles connected to a node) are uncorrelated. However, whether these degrees correlation exist in real networks and induce the explosive transition of information spreading at higher-order interactions is not very clear. Based on the real social networks data analysis, we find that the triangle degree increases with the independent edge degree approximatively as a power law, indicating a positive correlation between them. To understand how these correlations affect the spreading dynamics, we use an information-spreading model with higher-order interactions on synthetic networks and control the correlated strength of these degrees. Interestingly, our results reveal that the correlated structure would accelerate the information spreading with a fast-spreading speed. In addition, we uncover that the higher-order interactions will induce a discontinuous transition and that there is a bistable region with healthy and endemic states co-existing. Further, we discover that a highly correlated independent edge and triangle degrees will reduce the spreading threshold, which means the correlated structure promotes explosive information spreading. Finally, we utilize the microscopic Markov chain approach(MMCA) to explain the simulations. Our findings may shed some light on understanding the fast-spreading phenomenon of information in real life.

Mathematical modeling and dynamic analysis for cancer resistance incorporating persister cells

Drug resistance is a key impediment to cancer treatment, however, the resistance mechanism remains controversial. Experiment evidence indicated that persister cells, a subpopulation in a transient pseudo-dormant state, are posited to play a potential role in the emergence of resistance. In this study, we propose a novel mathematical model for describing the interactions among sensitive, persister, and resistant cells to qualitatively and quantitatively analyze how persister cells affect cancer evolution and unravel the underlying resistance mechanisms. The proposed model is validated by theoretical analysis and fitting of actual human CT scan and mice data. Theoretical analysis demonstrates the existence and stability of the multiple steady states, as well as the global asymptotical stability of a unique steady state. Furthermore, bifurcation analysis reveals that the key factors, including the apoptotic rate of sensitive cells and the transformation rate between sensitive and persister cells, induce bistable phenomenon and are characterized by double saddle–node and transcritical bifurcations. The bistable region indicates that persister cells under high stable steady state as a reservoir could promote the emergence of resistant cells conferring a proliferative advantage and conversely when they are in lower stable steady state, the source of resistant cells and resistance process will be controlled. Therefore, the first transcritical bifurcation point can be viewed as an early indicator to detect critical transitions from low resistance to high resistance. Together, the proposed model and quantitative results would provide new insights for searching for strategies in modulating and decreasing the risk of drug resistance.

Optical bistability and flip-flop function in feedback Fano laser.

Optical bistability has the potential to emulate the capabilities of electrical flip-flops, offering plenty of applications in optical signal processing. Conventional optical bistable devices operate by altering the susceptibility of a nonlinear medium. This method, however, often results in drawbacks such as large device size, high energy consumption, or long switching times. This work proposes an optical bistable device incorporating strong optical feedback into a Fano laser. This leads to multiple stable states and introduces a region of bistability between the inherent Fano mode and a feedback-induced Fabry-Perot mode. Unlike conventional bistable devices, the Fano system exploits strong field localization in a nanocavity to control the properties of one of the laser mirrors. This configuration means that switching states can be achieved by modulating the mirror's loss rather than changing the susceptibility of the active medium. Importantly, modulation can be implemented locally on a nanocavity, bypassing the need to adjust the entire laser system. This leads to fast flip-flop actions with low energy consumption. The feedback Fano laser can be embodied in a compact microscopic structure, thus providing a promising approach towards integrated all-optical computation and on-chip signal processing.

Impact of community networks with higher-order interaction on epidemic dynamics

Complex networks can be used to describe the propagation of epidemics among groups in which multiple individuals interact. However, pairwise interactions are often insufficient to describe the social propagation process. And studies have shown that there is a close relationship between network topology and epidemic dynamics. Therefore, we focuses on the effect of community networks with higher-order interactions on epidemic dynamics. The influence of the community network with high-order interaction on epidemic dynamics is studied by adjusting the structural parameters of the community network. The simulation results show that when the average degree and the community connection strength are constant, the number of communities will only affect the propagation speed without affecting the propagation scale and the propagation threshold. The increase of the average degree will accelerate the propagation speed, increase the propagation scale and reduce the propagation threshold. The increase of the community connection strength will accelerate the initial propagation speed, reduce the propagation threshold and have little effect on the propagation scale. The addition of higher-order interactions will reflect new phenomena, such as discontinuous transition and bistable regions. and the introduction of higher-order innteractions will increase the scale and speed of propagation.

Investigation of optical bistability in spheroidal core–shell nanocomposites with passive and active dielectric cores

We investigated how induced optical bistability (IOB) and bistability domain (BD) of spheroidal core–shell nanocomposites (NCs) are affected by the depolarization factor (L), metal fraction (p), and host matrix (ɛh). The NCs are composed of passive and active dielectric cores coated with a metallic shell and embedded in various host matrices. By employing Laplace’s equation and the Drude–Lorentz model, we calculated the electric field enhancement in various regions of the NCs and studied their IOB theoretically and numerically. The BD of the same NCs is investigated using the root analysis approach. The study reveals that when the value of L decreases, the bistable region of OB increases. However, when p increases at constant L and ɛh, the bistable region gets wider. When the value of ɛh increases, the IOB region is achieved at larger values of incident field. Moreover, the IOB produced was narrower in the passive dielectric core than in the active one, showing that the type of core material also influences the IOB of the core–shell NCs. When the value of L changes, the region of BD also changes in both types of cores. Similarly, changing the value of p in both types of cores causes the BD to vanish or emerge. Moreover, varying ɛh, BD is produced in the OB regions. Overall, the IOB and BD in each core are sensitive to changes in L, p, and ɛh. Varying these parameters leads to the possibility of tuning the bistable regions, which can be used in optical circuits, logic operations, and optical memory.

Synchronization regimes in the ring of rodent hippocampal neurons at limbic epilepsy

This study aims to consider an ensemble of hippocampal neurons coupled in a ring, which may be responsible for generation of the primary rhythm at limbic epilepsy. Methods. Model equations were solved numerically. To determine the areas of oscillatory and excitable regime existance for a single neuron, the bifurcation analysis for the leakadge conductivity parameter was performed. The coupling delays was not implemented directly, instead, inertia in the synapse was introduced. To determine the stability of generation some couplings were removed and parameter detunig was introduced. Results. In the single neuron model the bistability region was detected, in which a stable focus coexhists with a limit cycle. Two main synchronous regimes were detected. The first regime inherits frequency of individual oscillator, with a relatively small phase shift between oscillators in the ring. The frequency of the second regime depends on the number of neurons in the ring, with the phase shift between neighbor oscillators being equal to ratio of oscillation period and number of neurons. This second regime can occur both for the parameters corresponding to bistabler regime in the individual neuron and for the parameters at which the only existing attractor is stable focus. The second synchronous regime is preserved for parameter detuning of 2% from their absolute values. Conclusion. It was shown that in the mathematical model of the ring of hippocampal neurons, where all the main significant currents are taken into account for individual neurons, and their parameters can vary, there is an oscillatory mode, the frequency of which is determined by the length of the ring and synaptic conductivity, rather than by the parameters individual neuron. In this case, a small change in synaptic conductivity can lead to a sharp (2–7 times) change in the generation frequency.

In silico study of area fraction effects on the behaviour of a ferrogranulate layer in an orthogonal applied field

In our study, we explore ferrogranulate—a mix of glass and steel particles, specifically Stockmayer and repulsive spheres. Confined to a monolayer with three-dimensional rotation, magnetic particles respond to an external magnetic field applied orthogonal to the granulate plane. By varying the overall area fraction while maintaining a constant steel-to-glass bead ratio, we analyze cluster formation. Results show that concentration growth both slows cluster dynamics and increases the likelihood of larger clusters, hindering the response to the magnetic field. At low applied field values, our calculations suggest a bistable region at high concentrations, where droplet precursors form due to dipolar and steric interactions.

Impact of periodic vaccination in SEIRS seasonal model.

We study three different strategies of vaccination in an SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) seasonal forced model, which are (i) continuous vaccination; (ii) periodic short-time localized vaccination, and (iii) periodic pulsed width campaign. Considering the first strategy, we obtain an expression for the basic reproduction number and infer a minimum vaccination rate necessary to ensure the stability of the disease-free equilibrium (DFE) solution. In the second strategy, short duration pulses are added to a constant baseline vaccination rate. The pulse is applied according to the seasonal forcing phases. The best outcome is obtained by locating intensive immunization at inflection of the transmissivity curve. Therefore, a vaccination rate of 44.4% of susceptible individuals is enough to ensure DFE. For the third vaccination proposal, additionally to the amplitude, the pulses have a prolonged time width. We obtain a non-linear relationship between vaccination rates and the duration of the campaign. Our simulations show that the baseline rates, as well as the pulse duration, can substantially improve the vaccination campaign effectiveness. These findings are in agreement with our analytical expression. We show a relationship between the vaccination parameters and the accumulated number of infected individuals, over the years, and show the relevance of the immunization campaign annual reaching for controlling the infection spreading. Regarding the dynamical behavior of the model, our simulations show that chaotic and periodic solutions as well as bi-stable regions depend on the vaccination parameters range.

Bifurcation analysis of waning-boosting epidemiological models with repeat infections and varying immunity periods

We consider the SIRWJS epidemiological model that includes the waning and boosting of immunity via secondary infections. We carry out combined analytical and numerical investigations of the dynamics. The formulae describing the existence and stability of equilibria are derived. Combining this analysis with numerical continuation techniques, we construct global bifurcation diagrams with respect to several epidemiological parameters. The bifurcation analysis reveals a very rich structure of possible global dynamics. We show that backward bifurcation is possible at the critical value of the basic reproduction number, R0=1. Furthermore, we find stability switches and Hopf bifurcations from steady states forming multiple endemic bubbles, and saddle–node bifurcations of periodic orbits. Regions of bistability are also found, where either two stable steady states, or a stable steady state and a stable periodic orbit coexist. This work provides an insight to the rich and complicated infectious disease dynamics that can emerge from the waning and boosting of immunity.

Transformation of rotating dipole and vortex solitons in an anharmonic potential

We investigate the basic properties of dipole and vortex solitons, both quiescent and rotating, supported by the axially symmetric anharmonic potential in a medium with cubic-quintic nonlinearity. The static solitons exhibit nonmonotonous behavior in terms of propagation constant as a function, and feature bistability regions. In the rotating frame, the dipole solitons transform into vortex solitons and the topological charge increases gradually with the growth of rotation frequency. Linear stability analysis and direct simulations reveal that rotating dipole solitons with higher charges are more stable than those with lower charges. Meanwhile, dipole solitons can rotate persistently during propagation and preserve their shape over multiple rotation periods. Our findings provide an alternative way for the transformation to achieve dipole and vortex solitons with higher topological charges.

A Fractional-Order Memristive Two-Neuron-Based Hopfield Neuron Network: Dynamical Analysis and Application for Image Encryption

This paper presents a study on a memristive two-neuron-based Hopfield neural network with fractional-order derivatives. The equilibrium points of the system are identified, and their stability is analyzed. Bifurcation diagrams are obtained by varying the magnetic induction strength and the fractional-order derivative, revealing significant changes in the system dynamics. It is observed that lower fractional orders result in an extended bistability region. Also, chaos is only observed for larger magnetic strengths and fractional orders. Additionally, the application of the fractional-order model for image encryption is explored. The results demonstrate that the encryption based on the fractional model is efficient with high key sensitivity. It leads to an encrypted image with high entropy, neglectable correlation coefficient, and uniform distribution. Furthermore, the encryption system shows resistance to differential attacks, cropping attacks, and noise pollution. The Peak Signal-to-Noise Ratio (PSNR) calculations indicate that using a fractional derivative yields a higher PSNR compared to an integer derivative.