Bistable Behavior Research Articles

Analysis for a model incorporating [formula omitted]secretase inhibitor to explore the mechanism of ‘Amyloid-[formula omitted] rise’

The abnormal accumulation of amyloid-β (Aβ) is a key factor in the advancement of Alzheimer’s disease (AD), prompting the development of numerous strategies to reduce Aβ levels in the brain. Aβ is produced through the hydrolysis of amyloid precursor protein (APP), beginning with its cleavage by β-secretase to yield a C-terminal fragment, C99, which is further processed by γ−secretase to release Aβ. The crucial role of γ−secretase in Aβ synthesis has led to the creation of various γ−secretase inhibitors aimed at regulating Aβ concentrations. Nonetheless, experimental observations have reported a paradoxical ‘Aβ rise’ phenomenon, where lower concentrations of γ−secretase inhibitor paradoxically lead to increased Aβ levels, thereby complicating the development of these inhibitors. To elucidate the underlying mechanisms of ‘Aβ rise’, we constructed and analyzed a mathematical model incorporating γ−secretase inhibitor. Our analysis reveals bistable behavior driven by saddle–node bifurcation within the model. Through comprehensive analysis, we identified the conditions precipitating ‘Aβ rise’ and discovered that varying concentrations of γ−secretase inhibitor result in three distinct Aβ trends: (i) a consistent decrease, (ii) an initial increase followed by a decrease (‘Aβ rise’), and (iii) a decrease, subsequent increase, and final decrease. These trends are consistent with empirical findings. Our study further reveals that the emergence of ‘Aβ rise’ is primarily attributed to both lower η cleaving rate for APP and degradation rate of C99. Therefore, inhibiting ‘Aβ rise’ can be achieved by enhancing the η cleaving rate for APP and degradation rate of C99. These findings give new insights into the underlying mechanism of ‘Aβ rise’ and potential therapeutic strategies for treating AD.

Analysis of long transients and detection of early warning signals of extinction in a class of predator-prey models exhibiting bistable behavior.

In this paper, we develop a method of analyzing long transient dynamics in a class of predator-prey models with two species of predators competing explicitly for their common prey, where the prey evolves on a faster timescale than the predators. In a parameter regime near a singular zero-Hopf bifurcation of the coexistence equilibrium state, we assume that the system under study exhibits bistability between a periodic attractor that bifurcates from the singular Hopf point and another attractor, which could be a periodic attractor or a point attractor, such that the invariant manifolds of the coexistence equilibrium point play central roles in organizing the dynamics. To find whether a solution that starts in a vicinity of the coexistence equilibrium approaches the periodic attractor or the other attractor, we reduce the equations to a suitable normal form, and examine the basin boundary near the singular Hopf point. A key component of our study includes an analysis of the long transient dynamics, characterized by their rapid oscillations with a slow variation in amplitude, by applying a moving average technique. We obtain a set of necessary and sufficient conditions on the initial values of a solution near the coexistence equilibrium to determine whether it lies in the basin of attraction of the periodic attractor. As a result of our analysis, we devise a method of identifying early warning signals, significantly in advance, of a future crisis that could lead to extinction of one of the predators. The analysis is applied to the predator-prey model considered in Sadhu (Discrete Contin Dyn Syst B 26:5251-5279, 2021) and we find that our theory is in good agreement with the numerical simulations carried out for this model.

Controllable nonlinear effects in a hybrid magnonical semiconductor microcavity

We investigate the bistability properties of the magnomechanical system driven by an amplitude-modulated pump laser. The bistable behavior exhibits a characteristic magnon switching pattern. This behavior is studied for different values of system parameters. A distinct indication of energy transfer between the mechanical and magnon modes becomes evident while examining the mechanical displacement spectrum within the system. Further, by appropriately adjusting the system parameters, it is observed that the system in its steady state exhibits entanglement dynamics. These findings imply that this system holds potential applications in highly responsive magnon switches, magnon sensors, and quantum communication platforms.

Nonlinearly induced entanglement in dissipatively coupled optomechanical system

Nonlinearly induced steady-state photon–phonon entanglement of a dissipative coupled system is studied in the bistable regime. Quantum dynamical characteristics are analysed by solving the mean-field and fluctuation equations of the system. It is shown that dissipative coupling can induce bistable behaviour for the effective dissipation of the system. Under suitable parameters, one of the steady states significantly reduces the dissipative effect of the system. Consequently, a larger steady-state entanglement can be achieved compared to linear dynamics. Furthermore, the experimental feasibility of the parameters is analysed. Our results provide a new perspective for the implementation of steady-state optomechanical entanglement.

Numerical analysis of the bistable propagation of lean premixed hydrogen flames

Premixed hydrogen-air flames that propagate in slender channels have been recently found to be bistable in the limit of fuel-lean mixtures and non-negligible heat losses. Specifically, two stable configurations conformed by either a circular or a double-cell flame front arise for the same combination of controlling parameters (fuel mixture, heat transfer). Nevertheless, this multiplicity of solutions lacks a satisfactory explanation that predicts the formation of either one or another structure given a particular ignition transient. In this work, the analysis of a set of numerical simulations is offered to unveil the underlying physics controlling the bistable behavior. The formulation employed here proves that simplified one-step Arrhenius reaction and quasi-two-dimensional equations suffice to reproduce the complex dynamics, rendering three-dimensional effects and detailed chemical kinetics as second-order contributions that may be important, however, to provide exact quantitative results. Specifically, the initial temperature profiles and subsequent expansion of the flow field prescribe the growth of the flame front leading to different curvatures and sizes of the kernel that control the evolution into one of the canonical structures. Moreover, the achievement of double-cell flames require splitting and reorientation processes prior to pairing of isolated flames, which call for specific initialization conditions that enable these transient dynamics.

Penggabungan Ti<sub>3</sub>C<sub>2</sub>T<sub>x</sub> dalam Matriks Poli (Metil Metakrilat) untuk Aplikasi Memori Tidak Meruap

MXenes, with their unique surface properties and 2D structure, have demonstrated promising potential in electronic devices, particularly in memory storage. This study explored the potential of 2D Ti<sub>3</sub>C<sub>2</sub>T<sub>x</sub> for the nonvolatile memory (NVM) application. The simple solution process routes were used to fabricate the two-terminal bistable switching devices. The silver nanowires/nanocomposite/ITO structure was deposited on a glass substrate using spin coating and spray coating techniques. The Ti<sub>3</sub>C<sub>2</sub>T<sub>x</sub> MXene flakes were incorporated into a poly(methyl methacrylate) (PMMA) polymer host to form the nanocomposite and act as a charge-trapping layer. Meanwhile, PMMA acts as a dielectric layer. The measured current-voltage data showed a bistable current behavior with the presence of a memory window. The fabricated NVM memory devices were reprogrammable when the endurance test was performed and stable up to 1×104 s cycles with a distinct ON/OFF ratio of 103. The conduction mechanisms were identified using the curve-fitting method with double log plots of current-voltage (I-V) data. Based on the obtained I-V characteristics, various conduction mechanisms, especially Schottky and Poole-Frenkel emission, trapped charge limiting current, and space charge limited current, were proposed to be responsible for the bistable switching behavior. Thus, the results of this study provide an experimental basis for using MXene in non-volatile memory applications.

Modeling and Structural Analysis of MEMS Shallow Arch Assuming Multimodal Initial Curvature Profiles

The present investigation focuses on the design and mathematical modeling of a microelectromechanical (MEMS) mode-localized based sensor/actuator system. This device incorporates a sensitive clamped–clamped shallow arch microbeam with an initial curvature shaped to resemble one of the first two symmetric and asymmetric modes of free oscillations of a clamped–clamped beam. The analysis reveals that with a suitable arrangement of the initial shape of the device flexible electrode and a proper tuning of the maximum initial rise and the actuating dc load enables the transition to display certain bistable behavior. This could be a better choice to build a device with a large stroke. Furthermore, the generated data showed the occurrence of mode-veering, indicating a coupling between the concerned symmetric and asymmetric modes of vibrations, and offering the possibility for such a device to be used as a mode-localized MEMS-based sensor utilizing veering and crossing phenomena. Indeed, where a certain energy is exchanged between symmetric and asymmetric modes of a microbeam, it can be utilized to serve as a foundation for the development of a new class of highly precise resonant sensors that can capture, with a certain level of precision, any of the sensed signal amplitudes.

Mean-field theory of spin-crossover transition in elastic molecular crystals with Morse potential energy

The thermally bistable behavior of spin-crossover solids opens up prospects for their widespread use as information technology materials, sensors, or micro-refrigerators. In this paper, we build upon a mean-field model of spin-crossover transition in elastic Morse lattice. The phase transition caused by the short-range elastic intermolecular interaction is discussed using an Ising-like fictitious-spin formulation and mean-field theory.

Bi-stability in femtosecond laser ablation by MHz bursts

In this work, a bi-stable behavior of laser ablation efficiency and quality was controlled by fluence and burst length. The plasma shielding of incoming laser radiation caused sudden jumps with a significant decrease in ablation efficiency for every even number of pulses in the burst. The attenuation of incoming laser radiation by plasma created by the previous pulse was incorporated into the toy model of burst ablation efficiency. The mathematical recurrence relation has been derived for the first time, binding ablation efficiency for the next pulse with the efficiency of the previous pulse, which predicts bi-stability, as well as sudden jumps occurring in ablation efficiency depending on the number of pulses in burst with the response to changes of the control parameter of peak laser fluence in the pulse. The modeling results using new recurrence relation showed stable and bi-stable ablation efficiency depending on burst fluence and the number of pulses, which agreed well with experimental data. The extremely efficient laser ablation has been achieved by optimizing the shielding effect using three pulses in the burst.

Effect of realistic distributed loads on the bi-stable behavior of a pre-stressed aileron

AbstractWe study both experimentally and numerically the aeroelastic response of a pre-stressed curved aileron in a high Reynolds number flow undisturbed at infinity. The structure is designed to have a peculiar nonlinear behavior. Specifically, the aileron has only one stable equilibrium when the external forces are vanishing, but it is bistable when distributed aerodynamic loads are applied. Hence, for sufficiently high fluid velocities, another equilibrium branch is possible. We test a prototype of such an aileron in a wind tunnel. A sudden change (snap) of the shell configuration is observed when the fluid velocity exceeds a critical threshold: the snapped configuration is characterized by sensibly lower drag. However, when the velocity is reduced to zero, the structure recovers its initial shape. A similar nonlinear behavior can have important applications for drag-reduction strategies since the transition between a bluff body-like and a slender body-like behavior is controlled by the free-stream fluid velocity and does not require any external actuation.

Mechanical response of a novel square dome shell with bistable behavior: Improved analytical method and empirical model

In this study, a novel square dome-shaped shell with a fascinating bistable behavior is proposed, which is able to quickly switch to a new stable configuration within its elastic range under a certain load, due to its elastic instability. Compared to most circular shells currently studied, it is easier to arrange multiple structures in three-dimensional space to obtain multistable responses. Numerical and experimental methods were adopted for the study of the mechanical response of the square shell, and main influence parameters were also investigated. In addition, an improved piecewise fitting method is introduced to establish an empirical formula for predicting the mechanical response of bistable shells, which can be used to guide the design of bistable shells. Finally, two types of metamaterials, uniaxial compressible metamaterials and triaxial compressible metamaterials, are successfully designed according to the above theory, the typical behaviors of which are studied via simulations. This novel structure presented in this paper has broad application prospects in the fields of energy absorption and programmable deformation structures.

Bistability and chaotic behaviors in a 4D cancer oncolytic Virotherapy mathematical model: Pspice and FPGA implementations

Oncolytic viruses (OVs) exploit characteristics of mass cells and tumor-related reaction of the body to the presence of antigen, to lyse malignant cells and modulate the tumor microenvironment. However, the effective clinical utilization of these powerful treatment modules necessitates their logical control, especially in order to prevent solid and metastatic outgrowths. Hence, it is imperative to develop methods to protect a virus from the annihilating surroundings from the bloodstream when traveling to tumor locations. Our article reports on bistability and chaotic behavior in a 4D cancer virotherapy model. We find that unstable, stable and chaotic behaviors can appear in the model when tuning some of its parameters. With the help of the chart of dynamic behaviors in parameter spaces, numerical investigations of the system’s characteristics are analyzed followed by a discussion of the obtained results. It appears that the local transition change from an invariant one-torus (IT1) to its two-torus (IT2) counterpart can be found in the system and this undergoes a Neimark-Saker (NS) change of direction. As the increasing rate of immune effector enhance, the immune cells amount increases and as a consequence, the virotherapy dynamics becomes chaotic with a pronounced Lyapunov exponent. This can result to the failure of the virotherapy due to the interference of the immune cells with viruses. We also focus our study on the deign of ad-hoc electronic and Field Programmable Gate Arrays (FPGA) implementations of the cancer virotherapy’s model, to illustrate the obtained results.

Investigation of Bistable Behaviour of Initially Curved Rectangular Microplates

Investigation of Bistable Behaviour of Initially Curved Rectangular Microplates

Long-range ordering of velocity-aligned active polymers.

In this work, we study the effect of covalent bonding on the behavior of non-equilibrium systems with the active force acting on particles along their velocity. Self-ordering of single particles does not occur in this model. However, starting from some critical polymerization degree, the ordered state is observed. It is homogeneous and exhibits no phase separation. In the ordered state, the chains prefer a near-two-dimensional configuration and all move in one direction. Importantly, the self-ordering is obtained only at intermediate active force magnitudes. At high magnitudes, the transition from the disordered to ordered state is suppressed by the swelling of the chains during the transition, as we show by the transition kinetics analysis. We demonstrate the bistable behavior of the system in a particular range of polymerization degrees, amplitudes of active force, densities, and thermostat temperatures. Overall, we show that covalent bonding greatly aids the self-ordering in this active particle model, in contrast to active Brownian particles.

Dynamic all-optical memory switching based on atomic optical bistable behavior in a three level Λ-type atomic system

We theoretically investigate the atomic optical bistability (AOB) in a three-level Λ-type atomic system confined in a unidirectional optical ring cavity. The role of the intensity or detuning of the control field on AOB is explored, and results show that absorption, dispersion, and nonlinearity can be modified significantly by the control field due to quantum coherence and interference in multilevel atomic systems. Thus, tuning the intensity or detuning of the control field can manipulate the switch-up and switch-down thresholds, as well as the area of the bistable hysteresis loop. According to the controllability of AOB, we design various schemes to realize dynamical all-optical switching between the high and low outputs of two bistable curves for a fixed cavity input. In addition, dynamical all-optical memory switching can be implemented by adding a pulse sequence for the intensity or detuning of the control field. For appropriate parameters, such as the cooperative coefficient, the extinction ratio of the switching can be improved dramatically.

Fear induce bistability in an ecoepidemiological model involving prey refuge and hunting cooperation

This work included a prey-predator eco-epidemiological model where the predator exhibits hunting cooperation factor, and the infected prey exhibits refuge and fear factors. By merging these factors, we endeavor to prove a thorough comprehension of the underlying mechanisms that command the stability and dynamics of ecoepidemiological systems. Mathematically the positiveness and boundedness of system solution are established. Existence conditions of system equilibria and their stability are found and analyzed by testing the characteristic equations of the system. Also, numerical simulation is carried out and which showed bistability and different stability behavior of the system as results of the effect of the system’s parameters.

Analysis of the stationary probability density of a generalized and bistable van der Pol system excited by colored noise

The stochastic P-bifurcation behavior of bi-stability in a generalized van der Pol oscillator with the fractional damping under colored noise and thermal excitation is investigated. Firstly, using the principle of minimal mean square error and lin-earization method, the non-linear stiffness terms can be equivalent to a linear stiffness which is a function of the system amplitude, and the original system is simplified to an equivalent integer order van der Pol system. Secondly, the system amplitude stationary probability density function is obtained by the stochastic averaging, and then based on the singularity theory, the critical parametric con-ditions for the system amplitude stochastic P-bifurcation are found. Finally, the types of the stationary probability density function of the system amplitude are qualitatively analyzed in each area divided by the transition set curves. The con-sistency between the analytical results and the numerical results acquired from Monte-Carlo simulation also testifies the theoretical analysis in this paper and the method used in this paper can directly guide the design of the fractional order controller to adjust the response of the system.

Pathway dynamics to double-cell premixed flames in lean hydrogen–air mixtures

The propagation of premixed flames over lean hydrogen–air mixtures have been found to be bistable in recent studies, considering slender channels with non-negligible conductive heat losses. In particular, two stable configurations conformed by either a circular or a double-cell flame front arise for the same combination of controlling parameters (fuel mixture, channel size and thermal conductivity). Nevertheless, this multiplicity of solutions lacks a satisfactory explanation to predict the formation of either one structure or the other during a particular ignition transient. In this work, detailed analyses are performed over the unsteady evolution of a set of numerical simulations. Specifically, the initial temperature profiles (distribution and peak value) and subsequent expansion of the flow field prescribe the early growth of the flame front leading to different curvatures and sizes of the kernel that control the evolution into each of the canonical structures. This study explores the underlying physics controlling the final-stage bistable behavior. In particular, the local convective effects and interactions between fronts have been identified as the key causes to produce each of the two stably propagating flames. Frequently found division of kernels cannot ensure the formation of double cells, which require additional reorientation dynamics and merging events due to asymmetric seeding of flame fragments or to interaction with neighboring structures.

Effect of air preheating temperature on the dynamic behaviour of a swirled spray flame

The effects of the air inlet temperature on the dynamic behaviour of a spray flame are reported for different air flow rates. Dodecane droplets are generated through a pressurised nozzle and introduced in the combustion chamber fed with air via two co-rotating swirlers. The flow rate of dodecane is kept constant (1.24gs-1) while the air flow rate is changed from 28gs-1 to 35gs-1 and its temperature from 70°C to 220°C. Microphones are used to record the different dynamics observed while a camera and a Phase Doppler Anemometry system allow to monitor the flame and the fuel spray.For low flow rates (between 28gs-1 and 32gs-1, leading to an overall equivalence ratio ranging between 0.6 and 0.7), the pressure fluctuations start by increasing with an increase of the temperature until, for a given temperature, the pressure fluctuations suddenly drop. This threshold temperature depends on the air flow rate. When displaying the pressure fluctuation level as a function of the bulk velocity (taking both air flow rate and temperature into account), the curves collapse into a similar shape. The instability frequency monotonically increases with the bulk velocity. For high flow rates (between 32gs-1 and 35gs-1, leading to overall equivalence ratio ranging between 0.5 and 0.6), a hysteresis phenomenon is found. Pressure fluctuations are relatively high for constantly decreasing temperature conditions and have almost similar levels as those obtained for lower flow rates. When constantly increasing the temperature, the levels are much lower, showing a bi-stable behaviour for the pressure fluctuations at a given operating point. A simple analysis based on the acoustic energy balance equation allows to qualitatively retrieve the behaviour of the pressure fluctuations amplitude and frequency for the low flow rate cases.

A triboelectric-piezoelectric hybrid nanogenerator for rotational energy harvesting based on bistable cantilever beam

This study presents a triboelectric-piezoelectric hybrid nanogenerator for harvesting rotational energy based on a bistable cantilever beam. The nonlinear bistable behavior effectively enhances the collision force with the triboelectric nanogeneration (TENG) boundary, enlarges the effective contact area of the triboelectric functional materials, and significantly increases the deformation of the piezoelectric cantilever beam, thereby improving the overall electrical output performance of the system. Excessive deformation of the piezoelectric cantilevers is effectively constrained by the TENG boundary, which prevents the degradation and failure of the piezoelectric material. A prototype is prepared and verified experimentally. The effects of key parameters on the output performance are systematically analyzed. According to the results on the overall electrical output of hybrid nanogenerator with and without bistable behavior, the hybrid nanogenerator with bistable behavior achieved an energy density of 29.04 W/m3 at a rotational speed of 450 r/min, which is 2.65 times higher than that of the hybrid nanogenerator without bistable behavior. In addition, the rotational speed range is broadened by more than 1.5 times, and the prototype can realize self-powered temperature monitoring and wireless transmission. Overall, the proposed rotational energy harvester with a magnetic coupling cantilever bistable behavior and TENG boundary mechanism offers a novel means to improve the electrical performance of energy harvesting systems for self-powered internet of things.