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We study a on-off feedback method to control the dynamics of a radio physical oscillator having hidden coexisting attractors. The proposed time-varying on-off feedback effectively controls the multi-stability which acts in an on-off manner. We show that for suitable values of feedback strength, feedback active time ratio and time period, the coexisting chaotic and periodic dynamics of the system go to a mono-stable periodic state followed by a stable steady state. This transition from multiple attractors to a single attractor is confirmed by calculating bifurcation diagram, Lyapunov exponent and the basin size as a measure. We also illustrate the generation of chaotic attractor in the system using this scheme.

Among various environmental factors associated with triggering or exacerbating autoimmune response, an important role is played by infections. A breakdown of immune tolerance as a byproduct of immune response against these infections is one of the major causes of autoimmune disease. In this paper we analyse the dynamics of immune response with particular emphasis on the role of time delays characterising the infection and the immune response, as well as on interactions between different types of T cells and cytokines that mediate their behaviour. Stability analysis of the model provides insights into how different model parameters affect the dynamics. Numerical stability analysis and simulations are performed to identify basins of attraction of different dynamical states, and to illustrate the behaviour of the model in different regimes.

International audience; The multi-stability of composite shells often exhibits complex mechanical behaviors, accompanied by large deformation, strong nonlinearity and multiple equilibrium branches. We present a numerical framework for stability analysis of laminated composite shells, which is capable of efficiently computing nonlinear equilibrium paths and critical points, and effectively assessing the stability of the structure’s equilibrium. The computational framework is applied to investigate several multi-stability problems in cylindrical laminated shells. Good agreement is observed even in an “extreme” experimental case where the multi-stability is highly sensitive, and it is found that the precise approximation of the strain energy is crucial for accurate prediction of shell stability. This study is believed to provide a powerful alternative to other methods for the stability analysis and the design of advanced composite shell structures

The epithelial-mesenchymal transition (EMT) and the corresponding reverse process, mesenchymal-epithelial transition (MET), are dynamic and reversible cellular programs orchestrated by many changes at both biochemical and morphological levels. A recent surge in identifying the molecular mechanisms underlying EMT/MET has led to the development of various mathematical models that have contributed to our improved understanding of dynamics at single-cell and population levels: (a) multi-stability-how many phenotypes can cells attain during an EMT/MET?, (b) reversibility/irreversibility-what time and/or concentration of an EMT inducer marks the "tipping point" when cells induced to undergo EMT cannot revert?, (c) symmetry in EMT/MET-do cells take the same path when reverting as they took during the induction of EMT?, and (d) non-cell autonomous mechanisms-how does a cell undergoing EMT alter the tendency of its neighbors to undergo EMT? These dynamical traits may facilitate a heterogenous response within a cell population undergoing EMT/MET. Here, we present a few examples of designing different mathematical models that can contribute to decoding EMT/MET dynamics.

This paper presents the application of a probabilistic multi-stability assessment of a modified two-area system under the presence of low and high uncertainty sources. The stability of the network is assessed under four stability regimes: frequency, small-signal rotor angle, large-signal rotor angle, and long-term voltage. The probabilistic assessment is carried out using Monte Carlo simulation. Two cases considering low and high uncertainty are investigated. The obtained results are presented in the form of parallel coordinate plots so that the interaction between multiple stability regimes can be more easily understood. It is observed that the poor response of small-signal rotor angle stability generally corresponds to poor response of other stability types in low uncertainty case. However, once the level of uncertainty increases and more sources of uncertainty exist, this relationship is significantly changed.

Morse Things are Internet connected ceramic cups and bowls that communicate with each other in Morse Code. This ongoing research iteratively asks thing-centered questions of things and technology. A premise of the Morse Things is that any understanding of a thing or technology is unstable and arguably fragile. In this pictorial, we reflect on how we as researchers, in the course of doing research with the Morse Things, unexpectedly found ourselves literally entangled in the conceptual and physical fragility of the research. This pictorial describes our growing awareness of this instability, beginning with a kintsugi repair of a broken Morse Thing, our false confidence in our package design for shipping, and the difficulties to conceptualize the machine learning world that we ourselves created. We reflect on these experiences, and now see these as reminders of the inevitable fragility and instability of research on thing-perspectives.

Changes in the composition of the human microbiome are associated with health and disease. Some microbiome states persist in seemingly unfavorable conditions, e.g., the proliferation of aerobe-anaerobe communities in oxygen-exposed environments in wounds or small intestinal bacterial overgrowth. However, it remains unclear how different stable microbiome states can exist under the same conditions, or why some states persist under seemingly unfavorable conditions. Here, using two microbes relevant to the human microbiome, we combine genome-scale mathematical modeling, bioreactor experiments, transcriptomics, and dynamical systems theory, to show that multi-stability and hysteresis (MSH) is a mechanism that can describe the shift from an aerobe-dominated state to a resilient, paradoxically persistent aerobe-anaerobe state. We examine the impact of changing oxygen and nutrient regimes and identify factors, including changes in metabolism and gene expression, that lead to MSH. When analyzing the transitions between the two states in this system, the familiar conceptual connection between causation and correlation is broken and MSH must be used to interpret the dynamics. Using MSH to analyze microbiome dynamics will improve our conceptual understanding of the stability of microbiome states and the transitions among microbiome states.One sentence summaryMulti-stability and hysteresis (MSH) is a potential mechanism to describe shifts to and persistence of aerobe-anaerobe communities in the microbiome.

International audience; We revisit two-step mass-balance models of biological processes as met to describe numerous biological systems including the anaerobic digestion or the nitrification process in view of its global stabilization. We show that when a bi-stability occurs, it can be possible to globally stabilize the dynamics toward an unique positive equilibrium by increasing the dilution rate. We give sufficient conditions on the growth functions of the model for this situation to appear. This illustrates that for biological multi-step reactional systems, increasing the residence time (e.g. decreasing the input flow rate) may not be the only way to stabilize the dynamics.

A new five-dimensional chaotic system with extreme multi-stability is introduced in this article. The mathematical model is established, and numerical simulations are done. This dynamical system complicates incident of extreme multi-stability. Most significantly, relied on the mathematical model, the recently proposed system has a curve of equilibria that ends in the occurrence of hidden attractors. We examine the initial-condition-dependent dynamics of this system. We inspect that there is an unrestricted number of coexistent attractors, which signifies the occurrence of extreme multi-stability strictly. In addition, the extreme multi-stability according to initial condition is investigated consuming the Lyapunov exponent spectra and bifurcation diagrams. The existence of coexisting infinitely many attractors is displayed with phase portraits. In the end, we calculate and debate Kolmogorov–Sinai entropy in the chaotic system. We direct trying the Kolmogorov–Sinai technique of entropic inspection for the dynamics of the system.

The topic of hidden attractors is a very hot topic in nonlinear dynamics. Multi-stability is another important topic in that area. One recent important category of multi-stable systems is “systems with extreme multi-stability”. In this paper we introduce a new five-dimensional chaotic system with both hidden attractors and extreme multi-stability. Such systems are very rare in literature. Also, we show its feasibility by the help of electronic circuit implementation.

In this paper, we report a new chaotic jerk system which shows self-excited and hidden oscillations depending on its parameters. Dynamic analysis shows that the proposed system exhibits multi-stability and coexisting attractors. To study the effect of time delays on the multi-stability feature of the system, we introduce multiple time delays in the third state variable. Investigation of dynamical properties of the time-delayed system shows the disappearance of multi-stability. Such a feature has not been reported earlier in the literatures.

In this paper, we discuss how chaotic systems show the importance of imperfection. This happens through the butterfly effect. Then we discuss that chaotic systems with extreme multi-stability can much better demonstrate such importance. The reason is that in such systems not only the quantity of time-series is affected by butterfly effect, but also the quality of time-series is changed by small imperfections in parameters or initial conditions. We prove the importance of that difference better by comparing the efficiency of a newly proposed parameter estimation method on both an ordinary chaotic system and a chaotic system with extreme multi-stability.

Quantitative models may exhibit sophisticated behaviour that includes having multiple steady states, bistability, limit cycles, and period-doubling bifurcation. Such behaviour is typically driven by the numerical dynamics of the model, where the values of various numerical parameters play the crucial role. We introduce in this paper natural correspondents of these concepts to reaction systems modelling, a framework based on elementary set theoretical, forbidding/enforcing-based mechanisms. We construct several reaction systems models exhibiting these properties.

In this paper, a p53-Mdm2 mathematical model is analyzed to understand the biological implications of feedback loops in a p53 system. Results show that the model can undergo four types of codimension-3 Bogdanov–Takens bifurcations, including cusp, saddle, focus and elliptic. Specifically, we find new phenomena including the coexistence of four positive equilibria, two limit cycles, the coexistence of three stable states (two stable equilibria and one stable limit cycle, or three stable equilibria), a heteroclinic loop enclosing a smaller stable limit cycle and a larger stable limit cycle. These findings extend the understanding of the complex dynamics of the p53 system, and can provide some potential biological applications.

This paper conveys new results of a new finance chaotic system with three unstable balance points of which one balance point is a hyperbolic saddle while the other balance points are saddle-foci. The new finance chaotic system involves three nonlinearities of which one is quadratic, the other is quartic and the third is absolute function nonlinearity. As an application of the new finance chaotic system, integral sliding mode control is invoked to achieve synchronization of master-slave finance chaotic systems. MATLAB simulations are carried out to explain the main results of this research report.

A scheme for switching of the optical bistability (OB) and multi-stability (OM) in a dielectric slab doped with a three-level ladder-configuration n-doped semiconductor quantum well is simulated. It is shown that the bistable behavior of the system in dielectric slab can be controlled via amplitude or relative phase of applied fields. This optical system may provide some new possibilities for test the switching process.

We consider gradient systems with an increasing potential that depends on a scalar parameter. As the parameter is varied, critical points of the potential can be eliminated or created through saddle-node bifurcations causing the system to transit from one stable equilibrium located at a (local) minimum point of the potential to another minimum along the heteroclinic connections. These transitions can be represented by a graph. We show that any admissible graph has a realization in the class of two dimensional gradient flows. The relevance of this result is discussed in the context of genesis of hysteresis phenomena. The Preisach hysteresis model is considered as an example., Comment: 20 pages, 6 figures

The existence of more than two stable equilibrium shapes (multi-stability) of a thin body with magnetizable elastomer in some non-uniform magnetic fields is found theoretically. The method of the creation of such non-uniform magnetic fields (using electromagnetic coils) is proposed. The criterion of an unstable body equilibrium is obtained.

Deployable meta-implants aim to minimize the invasiveness of orthopaedic surgeries by allowing for changes in their shape and size that are triggered by an external stimulus. Multi-stability enables deployable implants to transform their shape from some compact retracted state to the deployed state where they take their full sizes and are load-bearing. We combined multiple design features to develop a new generation of deployable orthopaedic implants. Kirigami cut patterns were used to create bi-stability in flat sheets which can be folded into deployable implants using origami techniques. Inspired by Russian dolls, we designed multi-layered specimens that allow for adjusting the mechanical properties and the geometrical features of the implants through the number of the layers. Because all layers are folded from a flat state, surface-related functionalities could be applied to our deployable implants. We fabricated specimens from polylactic acid, titanium sheets, and aluminum sheets, and demonstrated that a deployment ratio of up to ≈2 is possible. We performed experiments to characterize the deployment and load-bearing behavior of the specimens and found that the above-mentioned design variables allow for adjustments in the deployment force and the maximum force before failure. Finally, we demonstrate the possibility of decorating the specimens with micropatterns.

Nonlinear structural behaviour offers a richness of response that cannot be replicated within a traditional linear design paradigm. However, designing robust and reliable nonlinearity remains a challenge, in part, due to the difficulty in describing the behaviour of nonlinear systems in an intuitive manner. Here, we present an approach that overcomes this difficulty by constructing an effectively one-dimensional system that can be tuned to produce bespoke nonlinear responses in a systematic and understandable manner. Specifically, given a continuous energy function E and a tolerance ϵ > 0, we construct a system whose energy is approximately E up to an additive constant, with L ∞ -error no more that ϵ . The system is composed of helical lattices that act as one-dimensional nonlinear springs in parallel. We demonstrate that the energy of the system can approximate any polynomial and, thus, by Weierstrass approximation theorem, any continuous function. We implement an algorithm to tune the geometry, stiffness and pre-strain of each lattice to obtain the desired system behaviour systematically. Examples are provided to show the richness of the design space and highlight how the system can exhibit increasingly complex behaviours including tailored deformation-dependent stiffness, snap-through buckling and multi-stability.

Origami designs offer extreme reconfigurability due to hinge rotation and facet deformation. This can be exploited to make lightweight metamaterials with controlled deployability and tunable properties. Here, we create a family of origami-inspired cellular metamaterials which can be programmed to have various stability characteristics and mechanical responses in three independent orthogonal directions. The cellular metamaterials were constructed from their origami unit cell that can have one or two admissible closed-loop configurations. The presence of the second closed-loop configuration leads to the emergence of bi-stability in the cellular metamaterial. We show that the stability and reconfigurability of the origami unit cell, and thus the constructed cellular metamaterials, can be programmed by manipulating the characteristic angles inherited from the origami pattern. Two examples of such programmable metamaterial with bi-stability in out-of-plane direction and anisotropic multi-stability in orthogonal directions are presented. Our study provides a platform to design programmable three-dimensional metamaterials significantly broadening the application envelope of origami.

International audience; The savanna biome encompasses a variety of vegetation physiognomies that traduce complex dynamical responses of plants to the rainfall gradients leading from tropical forests to hot deserts. Such responses are shaped by interactions between woody and grassy plants that can be either direct, disturbance-mediated or both. There has been increasing evidence that several vegetation physiognomies, sometimes highly contrasted, may durably coexist under similar rainfall conditions suggesting multi-stability or at least not abrupt transitions. These fascinating questions have triggered burgeoning modelling efforts which have, however, not yet delivered an integrated picture liable to furnish sensible predictions of potential vegetation at broad scales. In this paper, we will recall the key ecological processes and resulting vegetation dynamics that models should take into account. We will also present the main modelling options present in the literature and advocate the use of minimalistic models, capturing only the essential processes while retaining sufficient mathematical tractability and restricting themselves to a minimal set of parameters assessable from the overall literature.

This paper investigates the dynamics of immune response and autoimmunity with particular emphasis on the role of regulatory T cells (Tregs), T cells with different activation thresholds, and cytokines in mediating T cell activity. Analysis of the steady states yields parameter regions corresponding to regimes of normal clearance of viral infection, chronic infection, or autoimmune behaviour, and the boundaries of stability and bifurcations of relevant steady states are found in terms of system parameters. Numerical simulations are performed to illustrate different dynamical scenarios, and to identify basins of attraction of different steady states and periodic solutions, highlighting the important role played by the initial conditions in determining the outcome of immune interactions., Comment: 26 pages, 10 figures, accepted for publication in Int. J. Bif. Chaos

This study investigates the elastic multi-stability properties originated from origami folding. Specifically, it focuses on a space-filling architecture consisting of stacked Miura-ori sheets, which exhibits multiple stable states corresponding to different internal folding configurations. The fundamentally three-dimensional shape transformations from origami folding impart several unique properties that are unachievable from the lower dimensional mechanisms. They are (1) anisotropy-arrangement of the stable and unstable states fundamentally differs along different principle axes; (2) adaptability-stable states can be generated or eliminated via simple pressurization; and (3) asymmetry-the energy barrier of switching from one stable state to another can be significantly higher than the opposite switch, even though the two stable states have the same energy level. These unique stability properties could be harnessed to create a wide variety of adaptive functionalities, such as programmable stiffness, impulsive actuation, and mechanical diode effect. The purpose of this paper is to examine the physical origin of the three stability properties and their correlations to the origami design. Results of this of study can foster the creation of novel multi-functional structures and materials based on origami.

The optical bistability (OB) and multistability (OM) in an open Λ-type three-level atomic system inside a ring cavity are investigated. It is found that the ratio of atomic injections β and the exit rates r0 from cavity evidently affects the threshold intensity of OB and OM. The effect of incoherent pumping field on the OB and OM of a medium is discussed. We show that the bistable behavior of the open system significantly differs from that in a corresponding closed system, especially with an increase in the incoherent pump rate. The intensity threshold is reduced in an open system but increases in a closed system. In addition, the dependence of OB and OM in an open system on spontaneously generated coherence, the relative phase the between probe and coupling fields, the coupling-field intensity, and the cooperation parameter are briefly discussed.

Optical bistability (OB) and optical multi-stability (OM) of a four-level ?-type atomic system with two fold lower levels inside a unidirectional ring cavity is investigated. The effect of quantum interference arising from spontaneous emission and incoherent pumping on OB and OM is discussed. It is found that the threshold of OB and OM can be controlled by quantum interference mechanisms. In addition intensity of coupling field and the rate of an incoherent pumping field on behavior of OB and OM are then discussed.

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.

Scientific Reports 6: Article number: 21463; Published online 19 February 2016; Updated 09 May 2016 The original version of this Article contained errors in the Abstract. “In different SCN cells, oscillations of biochemical markers such as the expression-level of clock genes, are not synchronized but instead form slow circadian phase waves propagating over the whole cell population spatio-temporal struc- ture is a fixed property set by the anatomy of a given SCN.

We investigate the optical bistability (OB) and optical multi-stability (OM) in a four-level Y-type atomic system. It is found that the optical bistability can strongly be affected by intensity and frequency detuning of coupling and probe fields. The effect of spontaneously generated coherence on phase control of the OB and OM is then discussed. It has also been shown that the optical bistability can be switched to optical multi-stability just by the quantum interference mechanism and relative phase of applied fields.

The optical bistability (OB) and optical multi-stability (OM) in a four-level quantum dot molecule are investigated. The effect of tunnel coupling and the rate of incoherent pump on OB are then discussed. It is found that the OB threshold can be controlled via tunnel coupling and the rate of incoherent pump. We demonstrate that the voltage-controlled detuning can significantly affect the behavior of OB and OM, therefore the OM converts to OB only by the rate of incoherent pump. The results obtained can be used for the development of new types of nanoelectronic devices for realizing switching process.

With a series of mathematical models, we explore impacts of predation on a prey population structured into two age classes, juveniles and adults, assuming generalist, age-specific predators. Predation on any age class is either absent, or represented by types II or III functional responses, in various combinations. We look for Allee effects or more generally for multiple stable steady states in the prey population. One of our key findings is the occurrence of a predator pit (low-density “refuge” state of prey induced by predation; the chance of escaping predation thus increases both below and above an intermediate prey density) when only one age class is consumed and predators use a type II functional response —this scenario is known to occur for an unstructured prey consumed via a type III functional response and can never occur for an unstructured prey consumed via a type II one. In the case where both age classes are consumed by type II generalist predators, an Allee effect occurs frequently, but some parameters give also rise to a predator pit and even three stable equilibria (one extinction equilibrium and two positive ones—Allee effect and predator pit combined). Multiple positive stable equilibria are common if one age class is consumed via a type II functional response and the other via a type III functional response—here, in addition to the behaviours mentioned above one may even observe three stable positive equilibria—“double” predator pit. Some of these results are discussed from the perspective of population management.

Neurons in the pre-Botzinger complex within the mammalian brain stem play important roles in the generation of respiratory rhythms. Experimental observations show that some neurons can exhibit novel mixed bursting activities. In this paper, based on a mathematical model proposed by Butera, we show how the mixed bursting activities depend on the potassium current in the coupled pre-Botzinger complex. Using fast-slow decomposition and bifurcation analysis, we investigate the dynamics of mixed bursting, as well as the mechanisms of transition between different mixed bursting patterns. We find that mixed bursting involves different bistability, and it is the transition state of two types of regular burstings.

It is widely accepted for humans and higher animals that vision is an active process in which the organism interprets the stimulus. To find out whether this also holds for lower animals, we designed an ambiguous motion stimulus, which serves as something like a multi-stable perception paradigm in Drosophila behavior. Confronted with a uniform panoramic texture in a closed-loop situation in stationary flight, the flies adjust their yaw torque to stabilize their virtual self-rotation. To make the visual input ambiguous, we added a second texture. Both textures got a rotatory bias to move into opposite directions at a constant relative angular velocity. The results indicate that the fly now had three possible frames of reference for self-rotation: either of the two motion components as well as the integrated motion vector of the two. In this ambiguous stimulus situation, the flies generated a continuous sequence of behaviors, each one adjusted to one or another of the three references., Author summary Vision is considered an active process in humans and higher animals in which the stimulus is interpreted by the subject and can be perceived in different ways if it is ambiguous. We aimed to find out whether this also holds for lower animals, such as the fruit fly Drosophila melanogaster. To provide ambiguity, we exposed flies to transparent motion stimuli in a flight simulator and found their behavior to be multi-stable. These results show that the visual system of the fly can separate the individual components of a transparent motion stimulus, and that this kind of stimulus is ambiguous to the fly. The extent to which the fly shows component selectivity in its behavior depends on several properties of the stimulus, like pattern contrast and element density. The alternations between the different behaviors exhibit a stochasticity reminiscent of the temporal dynamics in human multi-stable perception.

This paper presents models for a tension-based, multi-stable, large displacement, compliant rolling-contact element (CORE). The models are capable of determining stress, strain, and retaining forces and are derived using a strain-energy approach. Models are compared to empirical results and the utility of these models is demonstrated in a case study. The case study demonstrates a device with multiple stable equilibrium positions and tests the fatigue properties of tension-stable CORE.

Inspired by the impulsive movements in plants, this research investigates the physics of a novel fluidic origami concept for its pressure-dependent multi-stability. In this innovation, fluid-filled tubular cells are synthesized by integrating different Miura- Ori sheets into a three-dimensional topological system, where the internal pressures are strategically controlled similar to the motor cells in plants. Fluidic origami incorporates two crucial physiological features observed in nature: one is distributed, pressurized cellular organization, and the other is embedded multi-stability. For a single fluidic origami cell, two stable folding configurations can coexist due to the nonlinear relationships among folding, crease material deformation and internal volume change. When multiple origami cells are integrated, additional multi-stability characteristics could occur via the interactions between pressurized cells. Changes in the fluid pressure can tailor the existence and shapes of these stable folding configurations. As a result, fluidic origami can switch between being mono-stable, bistable and multi-stable with pressure control, and provide a rapid ‘snap-through’ type of shape change based on the similar principles as in plants. The outcomes of this research could lead to the development of new adaptive materials or structures, and provide insights for future plant physiology studies at the cellular level.

Frequency comb generation in microresonators is considered beyond the meanfield approximation. We show the appearance of multi-valued stationary states and predict the existence of a novel type of super cavity solitons.

The ground state of an electronic system of compounds revealing photo-induced phase transitions might be regarded as a multiple-well, on-site potential. Different types of asymmetric, multi-stable potentials correspond to compounds of different types: to spin conversion systems and to charge transfer systems. Thermodynamic properties of one-dimensional lattice systems with an asymmetric on-site double well and triple well potential are then considered in quantum and classical approaches. Studying a variety of regimes, one finds that the key feature is a level of asymmetry distinguished as a shift type and shape type in limiting cases. Nearly singular behaviour of heat capacity in shape type systems indicates an entropy driven phase transformation.

In this paper, we present a multi-stable property in a bimesogenic cholesteric liquid crystal material with a proper chiral additive and check its potential as an energy saving transmissive type liquid crystal display (LCD) through its electro-optic characteristics. Experimental results show that the multi-stable characteristics in the fabricated cholesteric LC cell are very stable. Such multi-stable properties depend on the driving frequency, voltage, and field direction. The contrast ratio in the fabricated transmissive type cholesteric LC cell was 15:1, which is a result produced by voltage and frequency control.

Electrofluidic displays have been demonstrated with multi-stable states that enable on, off, or grey-scaled pixel states with zero holding power. We demonstrate operating principles and characterize optical, electrical and environmental performance. We also report other electrofluidic developments including device operation from − 30°C to 70 °C and 30 millisecond switching speeds at 25°C.