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All homoiothermic organisms are capable of maintaining a stable body temperature using various negative feedback mechanisms. However, current models cannot satisfactorily describe the thermal adaptation of homoiothermic living systems in a physiologically meaningful way. Previously, we introduced stress entropic load, a novel variable designed to quantify adaptation costs, i.e. the stress of the organism, using a thermodynamic approach. In this study, we use stress entropic load as a starting point for the construction of a novel dynamical model of human thermoregulation. This model exhibits bi-stable mechanisms, a physiologically plausible features which has thus far not been demonstrated using a mathematical model. This finding allows us to predict critical points at which a living system, in this case a human body, may proceed towards two stabilities, only one of which is compatible with being alive. In the future, this may allow us to quantify not only the direction but rather the extent of therapeutic intervention in critical care patients.

International audience; In this work, we consider a mathematical model of syntrophic relationship between two microbial species of the anaerobic digestion process including mortality (or decay) terms. We focus on the acetogenesis and hydrogenotrophic methanogenesis phases. Our study gives a quite comprehensive analysis of a syntrophic model by analyzing the joined effects of syntrophy relationship, mortality, substrate inhibition and input concentrations that were neglected in previous studies. Using a general class of growth rates, the necessary and sufficient conditions of existence and local stability of all steady states of the four-dimensional system are determined according to the operating parameters. This general model exhibits a rich behavior with the coexistence of two microbial species, the bi-stability, the multiplicity of coexistence steady states, and the existence of two steady states of extinction of the first species. The operating diagram shows how the model behaves by varying the control parameters and illustrates the effect of the inhibition and the new input substrate concentration (hydrogen) on the reduction of the coexistence region and the emergence of a bi-stability region. Similarly to the classical chemostat model, including the substrate inhibition can destabilize a two-tiered microbial 'food chain' where the stability depends on the initial condition.

With the consideration of electromagnetic induction generated by the difference of membrane potentials between two adjacent neurons, a five-dimensional (5-D) memristor-coupled FitzHugh–Nagumo (FHN)...

Purpose The purpose of this paper is to develop an field programmable gate array (FPGA)-based neuron circuit to mimic dynamical behaviors of tabu learning neuron model. Design/methodology/approach Numerical investigations for the tabu learning neuron model show the coexisting behaviors of bi-stability. To reproduce the numerical results by hardware experiments, a digitally FPGA-based neuron circuit is constructed by pure floating-point operations to guarantee high computational accuracy. Based on the common floating-point operators provided by Xilinx Vivado software, the specific functions used in the neuron model are designed in hardware description language programs. Thus, by using the fourth-order Runge-Kutta algorithm and loading the specific functions orderly, the tabu learning neuron model is implemented on the Xilinx FPGA board. Findings With the variation of the activation gradient, the initial-related coexisting attractors with bi-stability are found in the tabu learning neuron model, which are experimentally demonstrated by a digitally FPGA-based neuron circuit. Originality/value Without any piecewise linear approximations, a digitally FPGA-based neuron circuit is implemented using pure floating-point operations, from which the initial conditions-related coexisting behaviors are experimentally demonstrated in the tabu learning neuron model.

In this work, we study a non-autonomous differential equation model for the interaction of wild and sterile mosquitoes. Suppose that the number of sterile mosquitoes released in the field is a given nonnegative continuous function. We determine a threshold [Formula: see text] for the number of sterile mosquitoes and provide a sufficient condition for the origin [Formula: see text] to be globally asymptotically stable based on the threshold [Formula: see text]. For the case when the number of sterile mosquitoes keeps at a constant level, we find that the origin [Formula: see text] is globally asymptotically stable if and only if the constant number [Formula: see text] of sterile mosquitoes released in the field is above [Formula: see text].

Large-eddy simulations are used to investigate the origin of the wake asymmetry and symmetry behind notchback Ahmed bodies. Two different effective backlight angles, ${\beta _1} = 17.8\mathrm{^\circ }$ and ${\beta _2} = 21.0\mathrm{^\circ }$ , are simulated resulting in wake asymmetry and symmetry in flows without external perturbations, in agreement with previous experimental observations. In particular, the asymmetric case presents a bi-stable nature showing, in a random fashion, two stable mirrored states characterized by a left or right asymmetry for long periods. A random switch and several attempts to switch between the bi-stability are observed. The asymmetry of the flow is ascribed to the asymmetric separations and reattachments in the wake. The deflection of the near-wall flow structures behind the slant counteracting the asymmetry drives the wake to be temporarily symmetric, triggering the switching process of the bi-stable wake. The consequence of deflection that forces the flow structure to form on the opposite side of the slant is the decisive factor for a successful switch. Modal analysis applying proper orthogonal decomposition is used for the exploration of the wake dynamics of the bi-stable nature observed.

We develop a delay differential equation model for the interactive wild and sterile mosquitoes. Different from the existing modelling studies, we assume that only those sexually active sterile mosquitoes play a role for the interactive dynamics. We consider the cases where the release amount is either constant or described by a given function of time. For the constant releases, we establish a threshold of releases to determine whether the wild mosquito suppression succeeds or fails. We study the existence and stability of the model equilibria. When the releases are described by given functions, the trivial equilibrium is no longer globally but locally uniformly asymptotically stable if the amount of releases is below the threshold whereas it is still globally uniformly asymptotically stable if the release amount is above the threshold. Numerical examples demonstrating the model dynamical features and brief discussions of our findings are also provided.

This paper considers an eco-epidemiological model with disease in the prey population. The disease in the prey divides the total prey population into two subclasses, susceptible prey and infected prey. The model also incorporates fear of predator that reduces the growth rate of the prey population. Furthermore, fear of predator lowers the activity of the prey population, which reduces the disease transmission. The model is well-posed with bounded solutions. It has an extinction equilibrium, susceptible prey equilibrium, susceptible prey-predator equilibrium, and coexistence equilibria. Conditions for local stability of equilibria are established. The model exhibits fear- induced backward bifurcation and bistability. Extensive numerical simulations show the presence of oscillations and occurrence of chaos due to fear induced lower disease transmission in the prey population.

Bi-stable mechanisms are systems with two distinct stable equilibrium positions within their range of operation. They are capable of steadily staying in positions without external power input and require less energy to move to the next stable state because of their snap-through behavior. Diverse applications including switches, deployable structures, and reconfigurable robots can benefit from bi-stability characteristics. However, the complexity of implementation and the limitation of structure configuration have made it difficult to apply conventional bi-stable mechanisms to the structures that require rotational bi-stability. Thus, in this paper, we proposed an implementation method using cylindrical magnets for the rotational bi-stable mechanism. The proposed bi-stable mechanism consists of a revolute joint with two links; one is the rotational link and the other is the fixed link. It has rotational bi-stability through the magnetic force relationship between the array of magnets on each link. To identify the characteristics of the proposed bi-stable mechanism, a cylindrical permanent magnet is considered as an electromagnet model that consists of one ring with a virtual electric current. Consequently, the magnetic field of the cylindrical permanent magnet can be calculated using Biot-Savart law. Similarly, the magnetic force between two cylindrical permanent magnets of the electromagnet model is calculated using Lorentz force law. The criteria of the magnet array for symmetric bi-stability are proposed and the potential energy diagram of the rotation link is considered as the performance criterion to identify the stable state.

Motivated with various responses of world governments to COVID-19, here we develop a toy model of the dependence epidemics spreading on the availability of tests for disease. Our model, that we call SUDR+K, is based on usual SIR model, but it splits the total fraction of infected individuals into two components: those that are undetected and those that are detected through tests. Moreover, we assume that available tests increase at a constant rate from the beginning of epidemics but are consumed to detect infected individuals. Strikingly we find a bi-stable behavior between a phase with a giant fraction of infected and a phase with a very small fraction. We show that the separation between these two regimes is governed by a match between the rate of testing and a rate of infection spread at given time. We also show that the existence of two phases does not depend on the mathematical choice of the form of the term describing the rate at which undetected individuals are tested and detected. Presented research implies that a vigorous early testing activity, before the epidemics enters into its giant phase, can potentially keep epidemics under control, and that even a very small change in rate of testing can increase or decrease the size of the whole epidemics of various orders of magnitude. For the real application of realistic model to ongoing epidemics, we would gladly collaborate with field epidemiologists in order to develop quantitative models of testing process., Comment: 6 pages, 7 figures, Nonlinear Dyn (2020)

The friction-induced vibration of a novel slider-on-rotating-disc system is studied by a combination of numerical analysis on the theoretical model and experimental investigation on the test rig. In this system, the rotation of an L-shaped component couples with the friction-induced stick–slip vibration in the tangential direction and produces a state-dependent normal force. The numerical results of the dynamic responses by employing the Coulomb friction model and the friction model with Stribeck effect are both in good agreement with the experimental results, therefore the credibility of the numerical analysis on the theoretical dynamic model is validated. The bi-stability phenomenon, i.e., there is coexistence of a stable pure sliding response and a stable stick–slip limit cycle in a certain parameter range, is not only revealed in the numerical analysis but also observed experimentally. Moreover, a novel approach to constitute a non-uniform friction interface on the disc surface is explored for its efficacy in suppressing the friction-induced stick–slip vibration of the system also by both numerical analysis and experimental testing, namely, the disc surface is divided into sectors assigned with different friction properties. Both the numerical and experimental results show that the non-uniform friction interface of the disc with appropriate friction properties of these sectors can be an effective approach to diminish the range of the operating parameters where the stick–slip vibration occurs and thereby reduce the possibility of occurrence of stick–slip vibration in the system.

The prediction of flow past a generic ship has been performed using partially-averaged Navier–Stokes (PANS) turbulence model. The Reynolds number based on the width of the ship is . A detailed comparison with resolved large-eddy simulation (LES) solution and available experimental data is made for a better understanding of the capability of PANS in predicting the turbulent flow in the wake. The results show that PANS produces similar trends to those predicted by LES. However, a coarse grid resolution will lead PANS to act as unsteady Reynolds-averaged Navier–Stokes (URANS). Although the geometry is symmetric for the incoming flow at a zero yaw angle, bi-stable behaviour is observed in the wake, contributing to an asymmetric flow distribution on the heli-deck.

This paper reports the emergence of bi-stability in a third-order memristive Wien-bridge oscillator. By transforming the parallel RC feedback network into a series resistor and capacitor (RC) feedback network in the previous non-ideal voltage-controlled memristor emulator, an improved memristor emulator is proposed and its fingerprints are exhibited. And then through introducing the proposed emulator to replace the parallel resistor in the conventional Wien-bridge oscillator, an improved memristor-based third-order Wien-bridge oscillator is constructed. Based on its mathematical model, the initial condition-dependent dynamical behaviour is revealed by theoretical analyses and numerical simulations and further verified by hardware experiments, from which the emergence of bi-stability in the memristive oscillator is well demonstrated.

We apply the competitive model of Loxley and Robinson (Phys Rev Lett 102:258701, 2009. doi: 10.1103/PhysRevLett.102.258701 ) to the study of a special case of visual rivalry. Three-peaked inputs with maxima at symmetrical locations are introduced, and the role of three-bump configurations is then considered. The model yields conditions for what can be interpreted as a bistable percept analogous to the one-dimensional version of a competition between the central and flanking parts of an image.

Empirical evidence suggests that carry-over effects (COEs) can have a strong influence on the time evolution of populations. Here, COEs are defined as any event or process in one season that affects individual performance in a non-lethal manner during the following seasons. Our results have the potential to explain previously reported experimental results and to provide new biological phenomena. The population response to COEs is typically considerably more complicated than previously believed. We found that COEs that reduce the reproduction rates always decrease the population density. However, in the case of COEs that reduce the survival rates, there could be an increase in the population size. Regarding the dynamical behaviour, the impact of COEs is primarily associated with a stabilizing role in ecological research. However, this response is guaranteed only in COEs affecting the reproduction rate when the survival is density independent (or has a negligible density-dependent component). Interestingly, COEs have the potential to create bi-stability scenarios, particularly in COEs across multiple seasons.

Both electrodes and substrates are factors of great significance for the performance of ferroelectric tunnel junctions (FTJs) in designing functional nanodevices. To provide a comprehensive view on the polarization stability in FTJs due to the effects of an electrode and a substrate misfit strain, in this work we calculated more than 1000 FTJ structures by utilizing an ab initio density functional theory (DFT) method, via changing the symmetry of the FTJ structure (i.e., both asymmetric and symmetric FTJs), electrodes (including Au, Ag, Cu, Pt, Co, Fe, and SrRuO3), barrier thickness (ranging from 2 to 10 unit cells), polarization direction (both positive and negative polarizations) and epitaxial strain (i.e., −3%, −2.5%, −2%, −1.5% and −1%) as variables. This shows that the FTJs can exhibit quite diverse polarization bi-stability due to the combined effect of the electrode and strain control, which indicates diverse performance of the FTJs modulated by the electrode and strain. In particular, the polarization-mediated electrostatic potential in the barriers with different electrodes forecasts an electrode-tailored tunnel electroresistance effect. Our study provides guidance on the practical applications of FTJs with regard to the selection of electrodes and substrates.

VO 2 is a model material system which exhibits a metal to insulator transition at T = 67°C thus holds potential for future ultrafast storage. There is a controversy on whether the IMT in VO 2 is purely electronic, or is driven by lattice distortions. However, the purely electronic process is more meaningful in ultrafast switching. We found a new electron-phonon pathway for a purely reversible electronic transition in a true bi-stable fashion under specific conditions. This finding will prompt the design of future ultrafast electro-resistive non-volatile memory devices.

A broadband energy harvester using bi-stability and frequency up-conversion is introduced for the first time in a host-parasite shape inspired by the parasitic relationship in plants. A macro-buckled hosting beam is used to create bi-stability by compressing the beam in the axial direction; two piezoelectric micro-beams are amounted on the host beam as parasitic structures to absorb the low-frequency macro-beam kinetic energy and convert it to micro-beams’ high-frequency vibration at resonance. The design and operational principle are presented; a prototype was then fabricated and tested. The results illustrate the harvester is capable of harvesting low-amplitude vibration energy over a wide bandwidth at low frequencies. This design provides a potential solution for power supply in self-powered sensing applications in the Internet of Things.

In this study, we examine a rapid and reversible origami folding method by exploiting a combination of resonance excitation, asymmetric bi-stability, and active control. The underlying idea is that, by harmonically exciting a bi-stable origami at its resonance frequencies, one can induce rapid folding between its different stable equilibria with a much smaller actuation magnitude than static folding. To this end, we use a bi-stable water-bomb base as an archetypal example to uncover the underlying principles of dynamic folding based on numerical simulation and experimental testing. If the water-bomb initially settles at its “weak” stable state, one can use a base excitation to induce the intra-well resonance. As a result, the origami would fold and remain at the other “strong” stable state even if the excitation does not stop. The origami dynamics starting from the strong state, on the other hand, is more complicated. The water-bomb origami is prone to show inter-well oscillation rather than a uni-directional switch due to a nonlinear relationship between the dynamic folding behavior, asymmetric potential energy barrier, the difference in resonance frequencies, and excitation amplitude. Therefore, we develop an active feedback control strategy, which cuts off the base excitation input at the critical moment to achieve robust and uni-directional folding from the strong stable state to the weak one. The results of this study can apply to many different kinds of origami and create a new approach for rapid and reversible (self-)folding, thus advancing the application of origami in shape morphing systems, adaptive structures, and reconfigurable robotics.

In this paper, a fractional-order hyperchaotic system based on dual memristors is represented to analyze the nonlinear dynamic behaviors via replacing two coupled resistors with dual memristors. It is worthy to note that the fractional-order hyperchaotic system has two zero eigenvalues and three nonzero eigenvalues, therefore the equilibrium plane can be separated into diverse areas which indicates the hyperchaotic system is stable or chaotic. The simulation results illustrate that the initial states have a significant impact on the dynamic behaviors, which can be mirrored by the phase portraits, the bifurcation diagrams, the power spectrum and the time-domain waveform. In particular, the memristor initial boosting phenomenon is investigated in the proposed hyperchaotic system, which implies the memristor initial states determine the attractor offset boosting behaviors under various initial controllers. Clearly, it differs from the variable offset boosting behavior totally due to its multi-dimension and nonlinearity. Finally, numerical results under different initial controllers are exhibited to demonstrate the memristor initial boosting phenomenon. Moreover, a hardware circuit based on PSPICE software is fabricated and its experimental simulations is given to verify the dynamic behaviors effectively.

The objective of this study is to analyze a model of the chemostat involving the attachment and detachment dynamics of planktonic and aggregated biomass in the presence of a single resource. Considering the mortality of species, we give a complete analysis for the existence and local stability of all steady states for general monotonic growth rates. The model exhibits a rich set of behaviors with a multiplicity of coexistence steady states, bi-stability, and occurrence of stable limit cycles. Moreover, we determine the operating diagram which depicts the asymptotic behavior of the system with respect to control parameters. It shows the emergence of a bi-stability region through a saddle-node bifurcation and the occurrence of coexistence region through a transcritical bifurcation. Finally, we illustrate the importance of the mortality on the destabilization of the microbial ecosystem by promoting the washout of species., L'objectif de cette étude est d'analyser un modèle du chémostat impliquant la dynamique d'attachement et de détachement de la biomasse planctonique et agrégée en présence d'une seule ressource. En considérant la mortalité des espèces, nous donnons une analyse complète de l'existence et de la stabilité locale de tous les équilibres pour des taux de croissance monotones. Le modèle pré-sente un ensemble riche de comportements avec multiplicité d'équilibres de coexistence, bi-stabilité et apparition des cycles limites stables. De plus, nous déterminons le diagramme opératoire qui dé-crit le comportement asymptotique du système par rapport aux paramètres de contrôle. Il montre l'émergence d'une région de bi-stabilité via une bifurcation noeud col et l'occurrence d'une région de coexistence via une bifurcation transcritique. Enfin, nous illustrons l'importance de la mortalité sur la déstabilisation de l'écosystème microbien en favorisant le lessivage des espèces.

With the additional dimension, 4D printing is emerging as a novel technique to enable configuration switching in 3D printed items. In this paper, four major approaches, namely self-assembly of elements, deformation mismatch, bi-stability, and the Shape memory effect (SME), are identified as the generic approaches to achieve 4D printing. The main features of these approaches are briefly discussed. Utilizing these approaches either individually or in a combined manner, the potential of 4D printing to reshape product design is demonstrated by a few example applications.

The paper explores an eco-epidemiological model of a predator–prey type, where the prey population is subject to infection. The model is basically a combination of S-I type model and a Rosenzweig–MacArthur predator–prey model. The novelty of this contribution is to consider different competition coefficients within the prey population, which leads to the emergent carrying capacity. We explicitly separate the competition between non-infected and infected individuals. This emergent carrying capacity is markedly different to the explicit carrying capacities that have been considered in many eco-epidemiological models. We observed that different intra-class and inter-class competition can facilitate the coexistence of susceptible prey-infected prey–predator, which is impossible for the case of the explicit carrying capacity model. We also show that these findings are closely associated with bi-stability. The present system undergoes bi-stability in two different scenarios: (a) bi-stability between the planner equilibria where susceptible prey co-exists with predator or infected prey and (b) bi-stability between co-existence equilibrium and the planner equilibrium where susceptible prey coexists with infected prey; have been discussed. The conditions for which the system is to be permanent and the global stability of the system around disease-free equilibrium are worked out. Copyright © 2015 John Wiley & Sons, Ltd.

The electrostatic instability (pull-in) of a flat electrode in a parallel plate capacitor has been shown to be highly sensitive to external mechanical loads such as pressure. In this paper, we substantiate the possibility of prompting additional unstable configurations in such a system, with a remarkable sensitivity to the applied pressure. This additional instability has significant advantageous properties for sensing purposes. In addition to the high sensitivity and robustness of the pull-in voltage measurements, it can be adjusted so that after the unstable configuration is met, a snap-through to a new stable configuration occurs. As a result of this bi-stable behavior, the contact between the electrodes, which is the main drawback of pull-in phenomena, will be easily avoided. The results of this paper particularly suggest the suitability of this mechanism for two different methods of pressure measurements.

Evidence from paleo-proxy records suggests that the Atlantic Meridional Overturning Circulation (AMOC) can be in both an AMOC on state, the AMOC as we observe it today, and an AMOC off state, where the AMOC becomes extremely weak or even collapses. The freshwater transport due to the AMOC ($ M_{ov} $) at 34°S in the Atlantic has often been used as an indicator for bi-stability, with a positive $ M_{ov} $ suggesting a monostable AMOC and a negative $ M_{ov} $ suggesting a bi-stable AMOC. Often studies have shown that the sign of the divergence of the $ M_{ov} $ might be a good indicator of AMOC bi-stability. In this study we investigate how model bias affects the sign of $ M_{ov} $ across all latitudes in the Atlantic basin, through a detailed analysis of the Coupled Model Inter-Comparison Project 5 (CMIP5) model ensemble. $ M_{ov} $, in the CMIP5 models is generally too positive in the southern Atlantic due to a salinity bias, while in the subtropical North Atlantic the values of $ M_{ov} $ are influenced by a combination of velocity and salinity biases. We compare these results to observations, reanalysis products and Hadley Centre Global Environmental Model version 3 global configuration version 2, a current generation coupled model which exhibits a stable AMOC off state, and discuss the differences that can lead to the possibility of a bi-stable AMOC as opposed to a monostable AMOC.

Submitted to the Journal of the Mechanics and Physics of Solids (JMPS); International audience; We study a simple micro-mechanical device that does not lose its snap-through behavior in an environment dominated by fluctuations. The main idea is to have several degrees of freedom that can cooperatively resist the de-synchronizing effect of random perturbations. As an inspiration we use the power stroke machinery of skeletal muscles, which ensures at sub-micron scales and finite temperatures a spectacularly swift recovery of an abruptly applied slack. In addition to hypersensitive response at finite temperatures, our prototypical Brownian snap spring also exhibits criticality at special values of parameters which is another potentially interesting property for micro-scale engineering applications.

We analyze the robustness of a system-level genetic circuit which is constructed by a bottom-up strategy. The latest trend in synthetic biology is to create large-scale and complex genetic circuits realizing desired programmable functions. An approach for the creation is bottom-up construction, that is, well-characterized small-scale circuits are coupled into large-scale system-level circuits involving desired programmable functions that can be predicted from the modules. However, in general, an intrinsic property in a circuit may be broken by internally connecting external circuits. We analyze a successful circuit created by a bottom-up construction strategy to identify the reason behind a successful synthesis. Utilizing the robustness analysis method based on the structured singular value, we can guarantee the validity of the bottom-up construction.

Allelopathic stimulators have some stabilizing role for the interaction between two or more competitive phytoplankton species within aquatic environment. Various models within deterministic environment are examined by several researchers to understand the role of allelo-chemicals to shape the dynamic behavior within deterministic environment. As plankton species are available within aquatic environment so they are subjected to environmental driving forces. In the present paper we have considered an existing and well established two-species competitive phytoplankton model where one species is toxic. We have revealed various interesting dynamical features of the model which were overlooked in the earlier studies. The stochastic model considered in this paper is obtained from the deterministic model by introducing multiplicative white noise terms. For the stochastic model, we have established the existence of global solution which ensures positivity and boundedness of the solution starting from an interior point of first quadrant in presence of environmental driving forces. Bounds for different order moments of solution are obtained and used to prove the stochastic boundedness of solution. The sufficient conditions for stochastic permanence are obtained and verified with the help of numerical examples. Analytical results are interpreted from ecological point of view.

We have compared different types of natural self-organizing systems: crystal-like formation of multimolecular systems were conferred with self-organization in active media and dissipative structure formation. The comparison revealed a common feature of all such systems. They all have bi-(multi-)stable states. We propose a hypothesis that self-organization is impossible in systems that could not have bi-(multi-)stable states.

Following Levins’ patch occupancy model, we presented a differential-equation model, in which both the metapopulation dynamics and the dynamics of the fraction of suitable patches in the habitat are characterized. Habitat restoration induced by organism itself (internal restoration) and by other organisms or/and abiotic causes (external restoration) were incorporated in the model, together with habitat destruction. Stability analysis revealed the existence of alternative equilibriums (i.e., bi-stability) in the system. The internal restoration of habitat was identified as the trigger for the bi-stability, whereas the external restoration, in contrast, can eliminate the bi-stability from the system. The results, thus, emphasize the important role of the organism-environment feedback in biological conservation.

We consider a single impurity Anderson model (SIAM) in which the quantum dot(QD) is strongly coupled to a phonon bath in polaron regime. This coupling results in an effective e-e attraction. By computing the self energies using a current conserving approximation which is up to second order in this effective attraction, we show that if the interaction is strong enough, in non particle-hole (PH) symmetric case, the system would be bi-stable and we have hysteresis loop in the I–V characteristic. Moreover, the system shows negative differential conductance in some bias voltage intervals.

This paper investigates exploiting a bi-stable restoring force to enhance the transduction of wake-galloping energy harvesters in unsteady flows. To that end, a harvester consisting of a piezoelectric cantilever beam augmented with a square-sectioned bluff body at the free end is considered. Two repulsive magnets located at the tip of the beam are used to introduce the bi-stable restoring force. Unsteadiness is generated in a wind tunnel using static-grid structures located in the upstream of the bluff body. Three different mesh screens with square bars are designed with different bar and mesh widths to control the Reynolds numbers and associated unsteadiness. A series of wind tunnel tests are then used to experimentally investigate the response of the harvester with and without the tip magnets. Results demonstrate that the bi-stable restoring force can be used to improve the output power of the harvester under unsteady flow conditions.

In general, media coverage would not be implemented unless the number of infected cases reaches some critical number. To reflect this feature, we incorporate the media effect and a critical number of infected cases into the disease transmission rate and consider an susceptible-infected-susceptible epidemic model with logistic growth. Our model analysis shows that early media alert and strong media effects are preferable to decrease the numbers of infected cases at endemic equilibria. Furthermore, we noticed that the model may have up to three endemic equilibria and bi-stability can occur in a threshold interval for the critical number. Note that the interval depends on parameters for the focal disease and the media effect. It is possible to roughly estimate the interval for re-emerging diseases in a given region. Therefore, the result could be useful to health policymakers. Global stability is also obtained when the model admits a unique endemic equilibrium.

[Departement_IRSTEA]Ecotechnologies [TR1_IRSTEA]INSPIRE; International audience; We consider a model of two microbial species in a chemostat competing for a single-resource, involving the flocculation of the most competitive species which is present in two forms: isolated and attached. We first show that the model with one species and a non-monotonic growth rate of isolated bacteria may exhibit bi-stability and allows the appearance of unstable limit cycles through a sub-critical Hopf bifurcations due to the joined effect of inhibition and flocculation. We then show that the model with two species presents an even richer set of possible behaviors: coexistence, bi-stability and occurrence of stable limit cycles through a super-critical Hopf bifurcations. All these features cannot occur in the classical chemostat model, where generically at most one competitor can survive on a single resource.

It is increasingly evident that for a number of high-profile pathogens, transmission involves both direct and environmental pathways. Much of the distinguished evolutionary theory has, however, focused on each of transmission component separately. Herein, we use the framework of adaptive dynamics to study the evolutionary consequences of mixed transmission. We find that environmental transmission can select for increased virulence when direct transmission is low. Increasing the efficiency of direct transmission gives rise to an evolutionary bi-stability, with coexistence of different levels of virulence. We conclude that the overlooked contribution of environmental transmission may explain the curious appearance of high virulence in pathogens that are typically only moderately pathogenic, as observed for avian influenza viruses and cholera.

This paper introduces a novel treatment function into an SIR model with bi-linear infection force. Treatment is assumed to increase at a decreasing rate as the sub-population of infected rises. But at some finite number of infected individuals, society’s ability to treat the infected reaches a peak and then begins to fall, perhaps due to diminishing supplies or efficiency of health care resources. The system is found to have as many as four equilibria, with possible bi-stability, backward bifurcations, and limit cycles. Particular attention is paid to the effect of variations in the key treatment parameter, r . It is found that when r is either low or high, small changes in r do not affect the equilibrium outcome.

The stability of the predator–prey model subject to the Allee effect is an interesting topic in recent times. In this paper, we investigate the impact of weak Allee effect on the stability of a discrete-time predator–prey model with Holling type-IV functional response. The mathematical features of the proposed model are analyzed with the help of equilibrium analysis, stability analysis, and bifurcation theory. We provide sufficient conditions for the flip bifurcation by considering Allee parameter as the bifurcation parameter. We observe that the model becomes stable from chaotic dynamics as the Allee parameter increases. Further, we observe bi-stability behavior of the model between only prey existence equilibrium and the coexistence equilibrium. Our analytical findings are illustrated through numerical simulations.

Due to the increasing risk of drug resistance and side effects with large-scale antiviral use, it has been suggested to provide antiviral drugs only to susceptibles who have had contacts with infectives. This antiviral distribution strategy is referred to as 'targeted antiviral prophylaxis'. The question of how effective this strategy is in infection control is of great public heath interest. In this paper, we formulate an ordinary differential equation model to describe the transmission dynamics of infectious disease with targeted antiviral prophylaxis, and provide the analysis of dynamical behaviours of the model. The control reproduction number R(c) is derived and shown to govern the disease dynamics, and the stability analysis is carried out. The local bifurcation theory is applied to explore the variety of dynamics of the model. Our theoretical results show that the system undergoes two Hopf bifurcations due to the existence of multiple endemic equilibria and the switch of their stability. Numerical results demonstrate that the system may have more complex dynamical behaviours including multiple periodic solutions and a homoclinic orbit. The results of this study suggest that the possibility of complex disease dynamics can be driven by the use of targeted antiviral prophylaxis, and the critical level of prophylaxis which achieves ℛ(c)=1 is not enough to control the prevalence of a disease.

Generally, the occurrence of multiple attractors indicates that the multi-stability existing in a nonlinear dynamical system and the long-time motion behavior are essentially different, depending on which basin of attraction the initial condition belongs to. Up to now, due to the emergence of multi-stability, some particular memristor-based nonlinear circuits whose dynamical behaviors are extremely related to memristor initial conditions or other initial conditions have attracted considerable attention. By replacing linear or nonlinear resistors with memristor emulators in some already-existing oscillating circuits or introducing memristor emulators with different nonlinearities into these oscillating circuits, various memristor-based nonlinear dynamical circuits have been constructed and broadly investigated. Motivated by these considerations, we present a novel fifth-order voltage-controlled memristor-based Chua's chaotic circuit in this paper, from which a wonderful phenomenon of bi-stability is well demonstrated by numerical simulations and PSIM circuit simulations. Note that the bi-stability is a special kind of multi-stability, which is rarely reported in the memristor-based chaotic circuits.The proposed memristor-based Chua's chaotic circuit is constructed by inserting an inductor into the coupled resistor branch in series and substituting the Chua's diode with a voltage-controlled memristor in the classical Chua's circuit. Five-dimensional system model is established, of which the equilibrium point and its stability are investigated. Theoretical derivation results indicate that the proposed circuit owns one or three equilibrium points related to the circuit parameters. Especially, unlike the newly reported memristive circuit with bi-stability, the proposed memristor-based Chua's chaotic circuit has only one zero equilibrium point under the given parameters, but it can generate coexistent chaotic and periodic behaviors, and the bi-stability occurs in such a memristive Chua's circuit. By theoretical analyses, numerical simulations and PSIM circuit simulations, the bi-stability phenomenon of coexistent chaotic attractors and periodic limit cycles with different initial conditions and their formation mechanism are revealed and expounded. Besides, with the dimensionless system equations, the corresponding initial condition-dependent dynamical behaviors are further numerically explored through bifurcation diagram, Lyapunov exponents, phased portraits and attraction basin. Numerical simulation results demonstrate that the proposed memristive Chua's system can generate bi-stability under different initial conditions. The PSIM circuit simulations and numerical simulations are consistent well with each other, which perfectly verifies the theoretical analyses.

We study a chemostat model that describes competition between two species for two essential resources based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the monotone dynamical system theory. It is shown that the limiting system of the model basically exhibits the familiar Lotka-Volterra alternatives: competitive exclusion, coexistence, and bi-stability, and most of these results can be carried over to the original model.

The inclusion of a ligated ruthenium moiety to ethynyl spiropyran, 5′-ethynyl-1′,3′,3′-trimethyl-6-nitrospiro[chromene-2,2′-indoline], has been shown to increase the lifetime of the ring-opened merocyanine form twentyfold. Calculations suggest that the higher barrier to thermal reversion of the merocyanine form of the metal alkynyl complex arises from the capacity for greater delocalisation of charge consequent of the presence of the ruthenium moiety. The complex may provide a different switching mechanism to the 5,5′-dithienylperfluorocyclopentene electrode decoupling seen previously.

A new concept for a micro mechanical bi-stable switch is presented. The bi-stability is achieved by a mechanically pre-stressed toggle-lever. As bi-stability occurs only in a certain range of geometries for the given mechanical device, extensive FEM analysis (ANSYS) has been used to get a proper design of the switch and to optimise the layout for symmetrical switching behaviour, large stroke and low mechanical stress in the mechanical elements. An analytical model of the bi-stable switch has been developed which gives similar results as the FEM calculations. Switching between the bi-stable states is done electro-statically. The bi-stable switch has been realized using silicon-on-insulator (SOI)-technology. First experimental results show that such bi-stable toggle-lever switches can be utilized for direct multimode fibre switching where a stroke of about 100 μm is needed.

Collective behaviors in social insect societies often emerge from simple local rules. However, little is known about how these behaviors are dynamically regulated in response to environmental changes. Here, we use a compartmental modeling approach to identify factors that allow harvester ant colonies to regulate collective foraging activity in response to their environment. We propose a set of differential equations describing the dynamics of: (1) available foragers inside the nest, (2) active foragers outside the nest, and (3) successful returning foragers, to understand how colony-specific parameters, such as baseline number of foragers, interactions among foragers, food discovery rates, successful forager return rates, and foraging duration might influence collective foraging dynamics, while maintaining functional robustness to perturbations. Our analysis indicates that the model can undergo a forward (transcritical) bifurcation or a backward bifurcation depending on colony-specific parameters. In the former case, foraging activity persists when the average number of recruits per successful returning forager is larger than one. In the latter case, the backward bifurcation creates a region of bistability in which the size and fate of foraging activity depends on the distribution of the foraging workforce among the model׳s compartments. We validate the model with experimental data from harvester ants (Pogonomyrmex barbatus) and perform sensitivity analysis. Our model provides insights on how simple, local interactions can achieve an emergent and robust regulatory system of collective foraging activity in ant colonies.