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In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found: JAK2 V617F and one in the TET2 gene. Whether one mutation is present influences how the other subsequent mutation will affect the regulation of gene expression. In other words, when a patient carries both mutations, the order of when they first arose has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation, the Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. Combined, these observations are used to shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.

Recent advances in origami science and engineering have particularly focused on the challenges of dynamics. While research has primarily focused on statics and kinematics, the need for effective and processable dynamic models has become apparent. This paper evaluates various dynamic modelling techniques for rigid-foldable origami, particularly focusing on their ability to capture nonlinear dynamic behaviours. Two primary methods, the lumped mass–spring–damper approach and the energy-based method, are examined using a bistable stacked Miura-origami (SMO) structure as a case study. Through systematic dynamic experiments, we analyse the effectiveness of these models in predicting bistable dynamic responses, including intra- and interwell oscillations, in different loading conditions. Our findings reveal that the energy-based approach, which considers the structure's inertia and utilizes dynamic experimental data for parameter identification, outperforms other models in terms of validity and accuracy. This model effectively predicts the dynamic response types, the rich and complex nonlinear characteristics and the critical frequency where interwell oscillations occur. Despite its relatively increased complexity in model derivation, it maintains computational efficiency and shows promise for broader applications in origami dynamics. By comparing model predictions with experimental results, this study enhances our understanding of origami dynamics and contributes valuable insights for future research and applications. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'. [ABSTRACT FROM AUTHOR]

Mitigating traffic jams is a critical step for the betterment of the urban transportation system, which comprises a large number of interconnected routes to form an intricate network. To study the distinct features and complexities of vehicular flow, a network consisting of multiple-loops with a single intersection is considered a directed weighted graph. The governing equations for individual loop densities are derived using the principle of mass conservation, considering a data-driven flow-density relationship. Firstly, we examine the stability of a double-loop network and explore the traffic behavior using the macroscopic fundamental diagram (MFD) for different sets of parameters. Utilizing popular techniques of nonlinear dynamics, the existence of bistability, bifurcations, oscillations, and switching dynamics is demonstrated in the case of the triple-loop network. Further, bistability is characterized by plotting the basin of attraction diagram for the coexisting attractors. Our study reveals that an increase in the number of loop lines enriches the dynamical properties of vehicular traffic flow. It is observed that depending upon the initial density configuration, a loop network can show various phases, namely free flow, stop-and-go traffic jams, and loop congestion. Additionally, we show the presence of period-2 orbits in the case of the quadruple-loop system. [ABSTRACT FROM AUTHOR]

The control of light through all‐optical means is a fundamental challenge in nanophotonics and a key effect in optical switching and logic. The optical bistability effect enables this control and can be observed in various planar photonic systems such as microdisk and photonic crystal cavities and waveguides. However, the recent advancements in flat optics with wavelength‐thin optical elements require nonlinear elements based on metastructures and metasurfaces. The performance of these systems can be enhanced with high‐Q bound states in the continuum (BIC), which leads to intense harmonic generation, improved light‐matter coupling, and pushes forward sensing limits. This study reports enhanced thermo‐optical nonlinearity and the observation of optical bistability in an all‐dielectric metasurface membrane with BIC. Unlike many other nanophotonic platforms, metasurfaces allow for fine control of the quality factor of the BIC resonance by managing the radiative losses. This provides an opportunity to control the parameters of the observed hysteresis loop and even switch from bistability to optical discrimination by varying the angle of incidence. Additionally, this work proposes a mechanism of nonlinear critical coupling that establishes the conditions for maximal hysteresis width and minimal switching power, which has not been reported before. The study suggests that all‐dielectric metasurfaces supporting BICs can serve as a flat‐optics platform for optical switching and modulation based on strong thermo‐optical nonlinearity. [ABSTRACT FROM AUTHOR]

For animals to meet environmental challenges, the activity patterns of specialized oscillatory neural circuits, central pattern generators (CPGs), controlling rhythmic movements like breathing and locomotion, are adjusted by neuromodulation. As a representative example, the leech heartbeat is controlled by a CPG driven by two pairs of mutually inhibitory interneurons, heart interneuron (HN) half-center oscillators (HCO). Experiments and modeling indicate that neuromodulation of HCO navigates this CPG between dysfunctional regimes by employing a co-regulating inverted relation; reducing Na+/K+ pump current and increasing hyperpolarization-activated (h-) current. Simply reducing pump activity or increasing h-current leads to either seizure-like bursting or an asymmetric bursting dysfunctional regime, respectively. Here, we demonstrate through modeling that, alongside this coregulation path, a new bursting regime emerges. Both regimes fulfill the criteria for functional bursting activity. Although the cycle periods and burst durations of these patterns are roughly the same, the new one exhibits an intra-burst spike frequency that is twice as high as the other. This finding suggests that neuromodulation could introduce additional functional regimes with higher spike frequency, and thus more effective synaptic transmission to motor neurons. We found that this new regime co-exists with the original bursting. The HCO can be switched between them by a short pulse of excitatory or inhibitory conductance. In this domain of coexisting functional patterns, an isolated cell model exhibits only one regime, a severely dysfunctional plateau-containing, seizure-like activity. This aligns with widely reported notion that deficiency of inhibition can cause seizures and other dysfunctional neural activities. We show that along the coregulation path of neuromodulation, the high excitability of the single HNs induced by myomodulin is harnessed by mutually inhibitory synaptic interactions of the HCO into the functional bursting pattern. [ABSTRACT FROM AUTHOR]

In this paper, a three-dimensional (3D) Filippov SEIS epidemic model is proposed to characterize the impact of limited medical resources on disease transmission with discontinuous treatment functions. Qualitative analysis of non-smooth dynamical behaviors are performed on two subsystems and sliding modes. Criteria on the stability of various kinds of feasible equilibria and bifurcations, e.g., saddle-node bifurcation, transcritical bifurcation, and boundary equilibrium bifurcation, are established. The theoretical results are illustrated by numerical simulation, from which we find there could exist bistable phenomena, e.g., endemic and pseudo-equilibria, endemic equilibria of the two subsystems, or endemic and disease-free equilibria, even the basic reproduction numbers of two subsystems are less than 1. The disease spread is dependent both on the limited medical resources and latent compartment, which are more beneficial to effective disease control than planar Filippov and smooth models. [ABSTRACT FROM AUTHOR]

In this paper, we study a prey–predator–top predator food chain model with nonlinear harvesting of top predator. We have derived two important thresholds: the top predator extinction threshold and the coexistence threshold. We found that the top predator will die out if the nonlinear harvesting from predator to top predator is larger than the top predator extinction threshold. On the other hand, the prey, predator and top predator coexist if the nonlinear harvesting from predator to top predator is less than the coexistence threshold. While the parameter value of nonlinear harvesting from predator to top predator is between two critical thresholds, the system displays bistability phenomena, implying that the top predator species either die out or exist with the prey and predator species, which largely depend on the initial condition. Thus, a bistable interval exists between two critical thresholds, which is a significant phenomenon for the model. Meanwhile, we performed bifurcation analysis for the model, showing that the system would arise backward/forward bifurcation and saddle-node bifurcation and Hopf bifurcation. Finally, we performed numerical simulations to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

AbstractThis study shed light on the simultaneous effects of bistability and electrical resistor on the equivalent damping of a piezoelectric cantilever beam energy harvester. Damping coefficient has a direct effect on the frequency bandwidth of an oscillating system. This paper, extends the experimental-analytical balanced energy (BE) method to obtain the damping change due to bistability of a piezoelectric energy harvester. By using extended Hamilton principle and Euler-Lagrange formulation with nonlinear magnetic field relations, the governing equations of the system are derived. Then the equivalent BE viscous damping model was adopted and the equivalent damping term is achieved. In BE method, the test signals are registered into the proposed BE algorithm, then the equivalent viscous damping coefficient of the system will be obtained. In the end, the effects of bistability and electrical resistor of the power circuit of piezoelectric patch is discussed. According to the results, by increasing the bistability of the system, the equivalent damping of the system will also increase. Besides by escalation the value of electrical load in piezoelectric power circuit, the value of the equivalent damping coefficient reaches a maximum value. This behavior is originated from the extracted power of the system. [ABSTRACT FROM AUTHOR]

Summary: Ecologists are being challenged to predict how ecosystems will respond to climate changes. According to the Multi‐Colored World (MCW) hypothesis, climate impacts may not manifest because consumers such as fire and herbivory can override the influence of climate on ecosystem state. One MCW interpretation is that climate determinism fails because alternative ecosystem states (AES) are possible at some locations in climate space. We evaluated theoretical and empirical evidence for the proposition that forest and savanna are AES in Africa. We found that maps which infer where AES zones are located were contradictory. Moreover, data from longitudinal and experimental studies provide inconclusive evidence for AES. That is, although the forest‐savanna AES proposition is theoretically sound, the existing evidence is not yet convincing. We conclude by making the case that the AES proposition has such fundamental consequences for designing management actions to mitigate and adapt to climate change in the savanna‐forest domain that it needs a more robust evidence base before it is used to prescribe management actions. [ABSTRACT FROM AUTHOR]

Treeline is a global ecological phenomenon in which tree populations decline, often abruptly, above a specific elevation or latitude. Temperature is thought to be a key determinant of treeline because it affects the rates at which trees establish, grow, produce seeds, and die. As climate change causes temperature increases, treelines have been observed to move in response—but there is considerable variability. In this study, we present a general mathematical model that provides possible explanations for both the general patterns observed in treelines and some of the variation. Avoiding system-specific details, our model assumes simply that all life processes are temperature-dependent. We incorporate the possibility of positive or negative feedback, in which the presence of trees either increases or decreases the temperature at their location. Our results indicate that this feedback and the relationship between temperature thresholds for growth, seed production, and seedling establishment are the key determinants of tree line form and movement. The model also shows that under many conditions bistability is predicted: treeline can equilibrate at two different elevations under the same conditions, depending on the system's history. General, flexible models like ours are essential for generating a unifying theory of treeline form and dynamics across multiple ecosystems. [ABSTRACT FROM AUTHOR]

Abstract ABL602 2 + 1, a bispecific antibody with two distinct domains binding to CLL-1 on leukemias and CD3 on T cells, exhibits superior T cell activation and tumour lysing activity. Treatment outcomes of bispecific antibody rely on acute myeloid leukemia cell replication and antibody induced tumour lysing, but their quantitative relationship was unknown. Mathematical models are employed to quantitatively investigate HL-60 cell kinetics determined by bispecific antibody and tumour burden. First, we analysed cytotoxicity assay data testing HL-60 cell against bispecific antibody and T cells, and found efficiency of bispecific antibody induced tumour lysing increases but saturates with increase of HL-60 cell, T cell and bispecific antibody concentration. As a result, their interaction leads to bistable HL-60 cell kinetics; namely, at a given bispecific antibody and T cell concentration interval, HL-60 cell kinetics with small tumour burdens are inhibited but refractory to large tumour burdens. T cell concentration is strong negatively correlated with HL-60 cell concentration. With bispecific antibody clearance, observed bistable HL-60 cell kinetics still exists. Our finding explains observed phenomenon that bispecific antibody was less efficacious at high tumour burden even with enough activated cytotoxic CD8 + T cells. Maintaining high antibody concentration and preventing T-cell exhaustion are equivalently important to sustain long-term control.

In this paper, we investigate the existence and stability of periodic solutions of switching dynamical systems consisting of two sub-equations. We first establish a general criterion to determine the stability of periodic solutions; namely, we derive the conditions under which the periodic solution is locally asymptotically stable, globally asymptotically stable, or unstable. Next, we develop general theorems to count the number of periodic solutions and find the basins of attractions for the periodic solutions and the trivial solution, respectively. As applications, we analyze two biological models in recent literature. Our general theorems not only reproduce the existing results in a unified and simpler manner but also lead to new and complete dynamical results including bistability of the periodic solution and the trivial solution. Numerical examples are also given to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

The present study has focused on the examination of a Holling type III nonlinear mathematical model that incorporates the influence of fear and Michaelis–Menten‐type predator harvesting. The incorporation of fear with respect to the prey species has been observed to result in a reduction in the survival probability of the prey population and a concurrent reduction in the reproduction rate of the prey species. The existence and stability of ecologically significant equilibria have been ascertained through mathematical analysis. Emphasis within the proposed model primarily centers on numerical bifurcations of codimensions 1 and 2. Numerical validation has been performed on all simulated outcomes within the feasible range of parametric values. Dynamical characteristics of the model have subsequently undergone investigation through a series of numerical simulations, successfully revealing various forms of local and global bifurcations. In addition to the identification of saddle‐node, Hopf, Bogdanov–Takens, transcritical, cusp, homoclinic, and limit point cycle (LPC) bifurcations, the model has also demonstrated bistability and global asymptotic stability. These bifurcation phenomena serve as illustrative examples of the intricate dynamical behavior inherent to the model. Numerical validation through graphical representations has been utilized to elucidate the effects of factors such as fear, nonlinear predator harvesting, and predation rate on the dynamics of the interacting species under different parametric conditions. [ABSTRACT FROM AUTHOR]

The impact of predator‐driven fear on ecosystems is significant and can encompass both trophic (direct) and nontrophic (indirect) effects. Previous studies have shown that nontrophic fear effects have an important role in predator–prey dynamics. This study investigates the nontrophic fear effect on prey caused by generalist predators and explores optimal harvesting. We assume that the reproduction rate of prey is reduced due to the fear effect, and generalist predator follows Holling type II foraging strategy for predation. Additionally, we assume that predators are commercially valuable and harvested proportionately to their density. We demonstrate the existence of equilibrium points, their local and global stability, and bifurcation analysis. We observe that the model system undergoes a sequence of codimension one and codimension two bifurcations. Our results show that in the absence of predator harvesting, increasing levels of fear destabilize the predator–prey system, and controlled harvesting is beneficial for the coexistence of both populations. Also, the harvesting of predators may produce hydra and multiple hydra effects. We identify different types of bistability phenomena, which emphasize the importance of initial population size. Further, an optimal harvesting policy is also explored by formulating an optimal control problem (OCP). The harvesting cost‐functional is designed by incorporating the bionomic equilibrium state. We use Pontryagin's maximum principle and solve the OCP numerically. It is observed that implementing optimal harvesting not only contributes to the ecological benefits by maintaining a sustainable balance of predator–prey evolution but also plays a significant role in maximizing the economic benefits. [ABSTRACT FROM AUTHOR]

Electrostatically actuated MEMS plate devices have many potential applications as micro-actuators and highly sensitive sensors. Bistability may occur in microplate devices and it refers to two stable configurations for a single value of actuating load. In this work, bistable behaviour of initially curved rectangular microplates, under the electrostatic and mechanical load actuation, has been investigated. In which detail investigation of bistability in load-deflection equilibrium paths and their associated characteristics, and later, resonance frequency behaviour in bistable regions have been carried out. For this, the governing differential equations of an initially curved rectangular plate have been developed using Kirchhoff's plate theory, including von Karman nonlinearity. Then, Galerkin's principle has been used to develop reduced order model of the governing partial differential equation of motion. To validate the results of reduced order model, we have carried out finite element analysis using a software COMSOL Multiphysics. We have observed qualitatively distinct behaviour in bistability characteristics of electrostatically and mechanically actuated microplates. We have also observed high sensitivity near bistability points and these points can be tuned by varying device parameters. This investigation could potentially help design bistable MEMS devices. [ABSTRACT FROM AUTHOR]

We propose a population dynamical model for SARS-CoV-2 that takes into account mask compliance and effectiveness, in the context of saturated treatment. This model also considers reinfection and relapse among individuals with comorbidities. Our findings indicate that global mask usage, in conjunction with other public health measures, effectively reduces the basic reproduction number ( R 0 ). We establish the local and conditional global stability of the disease-free equilibrium point. Notably, the model exhibits intriguing behavior due to saturated treatment and reinfection. Under specific parameter conditions, it demonstrates multiple endemic equilibria when R 0 < 1 resulting and backward and forward bifurcation. We conduct sensitivity analysis to pinpoint the key factors influencing disease spread. The existence of multiple equilibria contributes to intricate and diverse dynamics, showcasing a variety of bifurcations and oscillations through Hopf bifurcation. Under specific conditions, global asymptotic stability for the unique endemic equilibrium, when it exists, is established. Among further nonlinear dynamics exhibited by the proposed model, we establish backward Hopf bifurcation, Hopf–Hopf bifurcation and saddle-node bifurcation. Bistability of the equilibrium points is also observed through forward hysteresis. Additionally we provide the impact of parameters most effective in reducing in COVID-19 spread. Numerical simulations of the theoretical findings are offered to validate the results. [ABSTRACT FROM AUTHOR]

This work is devoted to the technology developed by the authors that allows one for fixed values of parameters and tracing by parameters to calculate stationary solutions of systems with delay and analyze their stability. We discuss the results of applying this technology to the Marchuk–Petrov antiviral immune response model with parameter values corresponding to hepatitis B infection. The presence of bistability and hysteresis properties in this model is shown for the first time. [ABSTRACT FROM AUTHOR]

The expression level of a gene can vary between genetically identical cells under the same environmental condition—a phenomenon referred to as gene expression noise. Several studies have now elucidated a central role of transcription factors in the generation of expression noise. Transcription factors, as the key components of gene regulatory networks, drive many important cellular decisions in response to cellular and environmental signals. Therefore, a very relevant question is how expression noise impacts gene regulation and influences cellular decision‐making. In this Review, we summarize the current understanding of the molecular origins of expression noise, highlighting the role of transcription factors in this process, and discuss the ways in which noise can influence cellular decision‐making. As advances in single‐cell technologies open new avenues for studying expression noise as well as gene regulatory circuits, a better understanding of the influence of noise on cellular decisions will have important implications for many biological processes. [ABSTRACT FROM AUTHOR]

In this paper, taking into account the maturation period of prey, we propose a predator-prey model with time delay and fear effect. We confirm the well-posedness of the model system, explore the stability of the equilibria and uniform persistence of the model, and investigate Hopf bifurcations. Moreover, we also numerically explore the global continuation of the Hopf bifurcation. Interestingly, our results show that as the delay increases, the stable and unstable periodic solutions may both disappear and the unstable positive equilibrium may regain its stability. These results reveal how the maturation delay and the fear effect jointly impact the population dynamics of the predator-prey system. [ABSTRACT FROM AUTHOR]

The effect of fear, the hunting cooperative process, and Allee's impact on the behavior of an ecological system are investigated and discussed. The impact of the delay of the prey's response to the predation risk is included. The Leslie-Gower growth is used to describe the growth of the predator population. Firstly, the solutions' existence, positivity, and boundedness within the limits of a suitable region in the parametric space for all time are studied. The stability of all equilibrium points under the surrounding environmental effects is established. Moreover, the occurrence of a Hopf bifurcation is discovered. The stability of the bifurcating periodic dynamic and their dynamical properties are studied. Finally, the obtained theoretical results are confirmed and validated utilizing numerical simulation. It is observed that the system possesses a bi-stable behavior and a Hopf bifurcation. [ABSTRACT FROM AUTHOR]

Objective: Postsurgical seizure freedom in drug‐resistant epilepsy (DRE) patients varies from 30% to 80%, implying that in many cases the current approaches fail to fully map the epileptogenic zone (EZ). We aimed to advance a novel approach to better characterize epileptogenicity and investigate whether the EZ encompasses a broader epileptogenic network (EpiNet) beyond the seizure zone (SZ) that exhibits seizure activity. Methods: We first used computational modeling to test putative complex systems‐driven and systems neuroscience‐driven mechanistic biomarkers for epileptogenicity. We then used these biomarkers to extract features from resting‐state stereoelectroencephalograms recorded from DRE patients and trained supervised classifiers to localize the SZ against gold standard clinical localization. To further explore the prevalence of pathological features in an extended brain network outside of the clinically identified SZ, we also used unsupervised classification. Results: Supervised SZ classification trained on individual features achieved accuracies of.6–.7 area under the receiver operating characteristic curve (AUC). Combining all criticality and synchrony features further improved the AUC to.85. Unsupervised classification discovered an EpiNet‐like cluster of brain regions, in which 51% of brain regions were outside of the SZ. Brain regions in the EpiNet‐like cluster engaged in interareal hypersynchrony and locally exhibited high‐amplitude bistability and excessive inhibition, which was strikingly similar to the high seizure risk regime revealed by our computational modeling. Significance: The finding that combining biomarkers improves SZ localization accuracy indicates that the novel mechanistic biomarkers for epileptogenicity employed here yield synergistic information. On the other hand, the discovery of SZ‐like brain dynamics outside of the clinically defined SZ provides empirical evidence of an extended pathophysiological EpiNet. [ABSTRACT FROM AUTHOR]

In this paper, focusing on individualistic generalist predators and prey living in herds which coexist in a common area, we propose a generalization of a previous model, namely, a two-population system that accounts for the prey response to predator attacks. In particular, we suggest a new prey-predator interaction term with a denominator of the Beddington-DeAngelis form and a function in the numerator that behaves as N for small values of N, and as N α for large values of N, where N denotes the number of prey. We can take the savanna biome as a reference example, concentrating on large herbivores inhabiting it and some predators that feed on them. Only two conditionally stable equilibrium points have emerged from the model analysis: the predator-only equilibrium and the coexistence one. Transcritical bifurcations from the former to the latter type of equilibrium, as well as saddle-node bifurcations of the coexistence equilibrium have been identified numerically by using MATLAB. In addition, the model was found to exhibit bistability. Bistability is studied by using the MATLAB toolbox bSTAB, paying particular attention to the basin stability values. Comparison of coexistence equilibria with other prey-predator models in the literature essentially shows that, in this case, prey thrive in greater numbers and predators in smaller numbers. The population changes due to parameter variations were found to be significantly less pronounced. [ABSTRACT FROM AUTHOR]

In this paper, we employ computational analysis to investigate the long-term potentiation (LTP) and memory formation in synapses between neurons. We use a mathematical model describing the synaptic transmission as a signal transduction pathway with a positive feedback loop formed by diffusion of nitric oxide (NO) to the presynaptic site. We found that the model of synaptic transmission exhibits a hysteresis-like behavior, where the strength of synaptic transmission depends not just on instantaneous interstimulus intervals, but also on the history of activity. The switching between resting and memory states can be induced by physiologically relevant and moderate (less than 50%) changes in the duration of interstimulus intervals. [ABSTRACT FROM AUTHOR]

The pathogenesis of the inflammatory, chronic, and common skin disease psoriasis involves immune cells, skin cells (keratinocytes), and the cytokines they secrete. Hyperproliferation and abnormal differentiation of keratinocytes are hallmarks of the disease. The roles of cytokines such as TNFa, IL-15, IL-17, and IL-23 in psoriasis have been studied through mathematical/computational models as well as experiments. However, the role of proinflammatory cytokine IL-36 in the onset and progression of psoriasis is still elusive. To explore the role of IL-36, we construct a network embodying indirect cell-cell interactions of a few immune and skin cells mediated by IL-36 based on existing knowledge. We also develop a mathematical model for the network and perform a global sensitivity analysis. Our results suggest that the model is most sensitive to a parameter that represents the level of cytokine IL-36. In addition, a steady-state analysis of the model suggests that an increase in the level of IL-36 could lead to the hyperproliferation of keratinocytes and, thus, psoriasis. Our analysis also highlights that the plaque formation and progression of psoriasis could occur through either a gradual or a switch-like increase in the keratinocyte population. We propose that the switch-like increase would be due to a bistable behavior of the network toward either a psoriatic or healthy state and could be used as a novel treatment strategy. [ABSTRACT FROM AUTHOR]

AbstractInnovative designs for solar collectors have attracted substantial academic and industrial interests owing to the high efficiency of solar panels in the recent past. This paper proposes the analysis and numerical design of a novel solar collector model composed of bistable laminates bonded with Macro Fiber Composite (MFC) actuators and solar cells. The bistable cross-ply laminate serves as the steering mechanism in this design by providing multiple stable shapes for the innovative solar collector design. Bistable morphing structures have received growing interest in aerospace structures and wind turbines due to their rapid shape-changing ability in response to changes in operating conditions, and this paper aims to integrate them more into the solar energy sector. The snap-through and snap-back motion of bistable laminates can be controlled by the voltage inputs of MFC actuators. The change of bistable laminate shape holds the solar cell in a position approximately at the latitude angle of the place to capture maximum solar energy. A systematic finite element parametric study has been performed to identify the optimum size and location of MFC actuators to achieve an energy-efficient snap-through and snap-back transition. As a result, a numerical design of a solar collector with six bistable elements has been proposed. In order to check the feasibility of the proposed designs, a numerical study has been performed to evaluate the total energy output and to optimize the solar panel tilt angle. ASHRAE’s solar irradiation model proposed in the literature has been used to identify the optimum solar panel tilt angle for maximum annual solar irradiation. This innovative solar collector model has demonstrated promising results, holds the potential for widespread application across various engineering domains, and paves the way for increased adoption of intelligent structures in everyday life. [ABSTRACT FROM AUTHOR]

In this paper the bistability of a mathematical model for the control of an olive tree disease is studied. The basin of stability values were computed for three different pairs of bistable equilibrium points by using the software bSTAB. Moreover an extension of the software functionalities is made, first by approximating the shape of the attractors in three dimensions and second by extending the sensitivity study with respect to some important parameters of the numerical scheme, e.g. hyperparameters, to the two dimensional case. Analogously, the bifurcation diagram of the basin of stability values with respect to one parameter of the model was extended to the two dimensional case where two parameters of the model can vary simultaneously. Finally an approximation of the surfaces of the sensitivity analysis and bifurcation diagrams were made. [ABSTRACT FROM AUTHOR]

A driven‐dissipative system is considered, consisting of an atomic Bose‐Einstein condensates loaded into a 2D Hubbard lattice and coupled to a single mode of an optical cavity. Due to the interplay between strong, repulsive atomic interaction and the atom‐cavity coupling, the system exhibits several phases of atoms and photons including the atomic superfluid (SF) and supersolid (SS). The dynamical behavior of the system, where dissipation is included by means of Lindblad master equation formalism. Due to the discontinuous nature of the Dicke transition for strong atomic repulsion, extended co‐existence region of different phases are found. The resulting switching dynamics are investigated, particularly between the coexisting SF and SS phases, which eventually becomes damped by the dissipation. [ABSTRACT FROM AUTHOR]

Time of day affects how well the immune system responds to viral or bacterial infections. While it is well known that the immune system is regulated by the circadian clock, the dynamic origin of time-of-day-dependent immunity remains unclear. In this paper, we studied the circadian control of immune response upon infection of influenza A virus through mathematical modeling. Dynamic simulation analyses revealed that the time-of-day-dependent immunity was rooted in the relative phase between the circadian clock and the pulse of viral infection. The relative phase, which depends on the time the infection occurs, plays a crucial role in the immune response. It can drive the immune system to one of two distinct bistable states, a high inflammatory state with a higher mortality rate or a safe state characterized by low inflammation. The mechanism we found here also explained why the same species infected by different viruses has different time-of-day-dependent immunities. Further, the time-of-day-dependent immunity was found to be abolished when the immune system was regulated by an impaired circadian clock with decreased oscillation amplitude or without oscillations. [ABSTRACT FROM AUTHOR]

Tumor–immune system interactions are very complicated, being highly nonlinear and not well understood. A large number of tumors can potentially weaken the immune system through various mechanisms such as secreting cytokines that suppress the immune response. In this paper, we propose a tumor–immune system interaction model with a nonmonotonic immune response function and adoptive cellular immunotherapy (ACI). The model has a tumor-free equilibrium and at most three tumor-presence equilibria (low, moderate and high ones). The stability of all equilibria is studied by analyzing their characteristic equations. The consideration of nonmonotonic immune response results in a series of bifurcations such as the saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. In addition, numerical simulation results show the coexistence of periodic orbits and homoclinic orbits. Interestingly, along with various bifurcations, we also found two bistable scenarios: the coexistence of a stable tumor-free as well as a high-tumor-presence equilibrium and the coexistence of a stable-low as well as a high-tumor-presence equilibrium, which can show symmetric and antisymmetric properties in a range of model parameters and initial cell concentrations. The new findings indicate that under ACI, patients can possibly reach either a stable tumor-free state or a low-tumor-presence state in the presence of nonmonotonic immune response once the immune system is activated. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Bistable autoactivation has been proposed as a mechanism for cells to adopt binary fates during embryonic development. However, it is unclear whether the autoactivating modules found within developmental gene regulatory networks are bistable, unless their parameters are quantitatively determined. Here, we combine in vivo live imaging with mathematical modeling to dissect the binary cell fate dynamics of the fruit fly pair-rule gene fushi tarazu (ftz), which is regulated by two known enhancers: the early (non-autoregulating) element and the autoregulatory element. Live imaging of transcription and protein concentration in the blastoderm revealed that binary Ftz fates are achieved as Ftz expression rapidly transitions from being dictated by the early element to the autoregulatory element. Moreover, we discovered that Ftz concentration alone is insufficient to activate the autoregulatory element, and that this element only becomes responsive to Ftz at a prescribed developmental time. Based on these observations, we developed a dynamical systems model and quantitated its kinetic parameters directly from experimental measurements. Our model demonstrated that the ftz autoregulatory module is indeed bistable and that the early element transiently establishes the content of the binary cell fate decision to which the autoregulatory module then commits. Further in silico analysis revealed that the autoregulatory element locks the Ftz fate quickly, within 35 min of exposure to the transient signal of the early element. Overall, our work confirms the widely held hypothesis that autoregulation can establish developmental fates through bistability and, most importantly, provides a framework for the quantitative dissection of cellular decision-making.

For animals to meet environmental challenges, the activity patterns of specialized oscillatory neural circuits, central pattern generators (CPGs), controlling rhythmic movements like breathing and locomotion, are adjusted by neuromodulation. As a representative example, the leech heartbeat is controlled by a CPG driven by two pairs of mutually inhibitory interneurons, heart interneuron (HN) half-center oscillators (HCO). Experiments and modeling indicate that neuromodulation of HCO navigates this CPG between dysfunctional regimes by employing a co-regulating inverted relation; reducing Na+/K+ pump current and increasing hyperpolarization-activated (h-) current. Simply reducing pump activity or increasing h-current leads to either seizure-like bursting or an asymmetric bursting dysfunctional regime, respectively. Here, we demonstrate through modeling that, alongside this coregulation path, a new bursting regime emerges. Both regimes fulfill the criteria for functional bursting activity. Although the cycle periods and burst durations of these patterns are roughly the same, the new one exhibits an intra-burst spike frequency that is twice as high as the other. This finding suggests that neuromodulation could introduce additional functional regimes with higher spike frequency, and thus more effective synaptic transmission to motor neurons. We found that this new regime co-exists with the original bursting. The HCO can be switched between them by a short pulse of excitatory or inhibitory conductance. In this domain of coexisting functional patterns, an isolated cell model exhibits only one regime, a severely dysfunctional plateau-containing, seizure-like activity. This aligns with widely reported notion that deficiency of inhibition can cause seizures and other dysfunctional neural activities. We show that along the coregulation path of neuromodulation, the high excitability of the single HNs induced by myomodulin is harnessed by mutually inhibitory synaptic interactions of the HCO into the functional bursting pattern.

We study the steady-state non-Hermitian magnomechanical system driven by a transverse magnetic field directly interacting with YIG sphere yielding in magnons excitation, which later interacts with cavity microwave photons. To make the system non-Hermitian, we use a traveling field directly interacting with magnons generating gain to the system. We start by illustrating PT-configuration of the system containing two PT broken regions around exceptional point and PT protected region along the axis of exceptional point. We discover that the steady-state population of cavity photons and magnons show bistable behavior depending upon the PT configuration, which becomes more significant as the values of the magnon–photon coupling and traveling field strength increases. We illustrate that steady-state photon only shows bistable behavior when the system in lossy PT broken configuration, means strength of traveling field is less than the magnon–photon coupling. Otherwise, it will just contain a single stable state because of bistability suppression with gain in the system, which is unlike with any other investigation in this direction. Further, a larger magnon–photon coupling increases photon intensity and decreases magnon intensity, because of photon and magnon energy exchange, leading to enhanced photon bistablity and decreased magnon bistability. However, in case of increasing strength of traveling field, both photon as well as magnon bistability is appeared to be decreasing. We also study the steady-state effective potential of the system and illustrate the occurrence of bistability with nonlinear interactions between contour trajectories, which similarly depends on the PT broken configuration of the system.

In this paper, focusing on individualistic generalist predators and prey living in herds which coexist in a common area, we propose a generalization of a previous model, namely, a two-population system that accounts for the prey response to predator attacks. In particular, we suggest a new prey-predator interaction term with a denominator of the Beddington-DeAngelis form and a function in the numerator that behaves as $ N $ for small values of $ N $, and as $ N^{\alpha} $ for large values of $ N $, where $ N $ denotes the number of prey. We can take the savanna biome as a reference example, concentrating on large herbivores inhabiting it and some predators that feed on them. Only two conditionally stable equilibrium points have emerged from the model analysis: the predator-only equilibrium and the coexistence one. Transcritical bifurcations from the former to the latter type of equilibrium, as well as saddle-node bifurcations of the coexistence equilibrium have been identified numerically by using MATLAB. In addition, the model was found to exhibit bistability. Bistability is studied by using the MATLAB toolbox bSTAB, paying particular attention to the basin stability values. Comparison of coexistence equilibria with other prey-predator models in the literature essentially shows that, in this case, prey thrive in greater numbers and predators in smaller numbers. The population changes due to parameter variations were found to be significantly less pronounced.

Fading memory is the capability of a physical system to approach a unique asymptotic behaviour, irrespective of the initial conditions, when stimulated by an input from a certain class. Standard stimuli from the AC periodic class typically induce fading memory effects in non-volatile memristors, as uncovered for the first time back in 2016. Very recently, a deep investigation of resistance switching phenomena in a TaOx resistive random access memory cell revealed the capability of the nano-device to exhibit one of two possible oscillatory behaviours, depending upon the initial condition, when subject to a particular periodic excitation. This interesting finding was, however, left unexplained. Bistability is the simplest form of local fading memory. In a system, endowed with local fading memory under a given stimulus, the initial condition does not affect the long-term behaviour of the state as long as it is drawn from the basin of attraction of either of the distinct coexisting state-space attractors (two limit cycles for the periodically forced memristor acting as a bistable oscillator). Here, the history of the system, encoded in the initial condition, is, thus, erasable only locally through ad hoc stimulation. Motivated by the discovery of local history erase effects in our resistive random access memory cell, this study applies a powerful system-theoretic tool, enabling the analysis of the response of first-order systems to square pulse train-based periodic stimuli, known as the time-average state dynamic route, to an accurate physics-based mathematical model, earlier fitted to the nano-device, to determine a strategy for specifying the parameters of an excitation signal, consisting of the sequence of two square pulses of opposite polarity per period so as to induce various forms of monostability or multistability in the non-volatile memristor. In particular, as an absolute novelty in the literature, experimental measurements validate the theoretical prediction on the capability of the device to operate as one of two distinct oscillators, depending upon the initial condition, under a specific pulse train excitation signal. The coexistence of multiple oscillatory operating modes in the periodically forced resistive random access memory cell, an example par excellence of their unique nonlinear dynamics, may inspire the development and circuit implementation of novel sensing and mem-computing paradigms. [ABSTRACT FROM AUTHOR]

This paper centers on the analysis of the dynamics of a modified Leslie–Gower predator–prey model employing Holling-type II schemes, with the prey exhibiting pure random diffusion and the predator undergoing a mixed form of movement. The extinction of species and uniform persistence of this system are explored, and several conditions for the stability, uniqueness and multiplicity of positive steady-state solutions are derived. In contrast to the specialist and generalist predator–prey systems in open advective environments, the dynamics of this system are more intricate. It emerges that multiple positive steady-state solutions and the bistable phenomenon exist for this system when a small advection rate and a moderate predation rate are imposed. Numerical simulations reveal that the increase of diffusion rate for prey disadvantages the survival of itself and has no impact on predator invasion, while the increase of diffusion rate for predators favors the invasion of itself. [ABSTRACT FROM AUTHOR]

Sleep is a universal, essential biological process. It is also an invaluable window on consciousness. It tells us that consciousness can be lost but also that it can be regained, in all its richness, when we are disconnected from the environment and unable to reflect. By considering the neurophysiological differences between dreaming and dreamless sleep, we can learn about the substrate of consciousness and understand why it vanishes. We also learn that the ongoing state of the substrate of consciousness determines the way each experience feels regardless of how it is triggered—endogenously or exogenously. Dreaming consciousness is also a window on sleep and its functions. Dreams tell us that the sleeping brain is remarkably lively, recombining intrinsic activation patterns from a vast repertoire, freed from the requirements of ongoing behavior and cognitive control. The paper by Tononi et al. discusses what sleep reveals about the substrate of consciousness, how experience can vanish during sleep, and how dreams can be supported by a brain largely disconnected from the environment, unreflective, and forgetful. [ABSTRACT FROM AUTHOR]

Predator foraging facilitation or hunting cooperation and the antipredator behavior of prey are essential mechanisms in evolutionary biology and ecology and may strongly influence the predator–prey dynamics. In a real-world scenario, this behavioral tendency is well documented, but less is known about how it could affect the dynamics between predator and prey. Here, we investigate the impact of the fear of predator on prey and the hunting cooperation in predator on the predator–prey dynamics, where the predator is assumed to be of generalist type. We observe that without fear, even with the high level of hunting cooperation, both populations may coexist, though the increasing level of hunting cooperation reduces the prey density at coexistence equilibrium. Moreover, increasing level of fear also destabilizes the system with and without hunting cooperation. Further, in the presence of hunting cooperation and fear effect, the model shows three different types of bistability phenomena: bistability between two coexisting equilibria, bistability between coexisting equilibria and prey-free equilibrium, and bistability between stable limit cycle and coexisting equilibria. In addition, saddle-node, Hopf, transcritical bifurcation of codimension one, Bautin (generalized Hopf), Bogdanov–Takens, and cusp bifurcation of codimension two are observed. [ABSTRACT FROM AUTHOR]

Generalist predation generally stabilizes the prey–predator dynamics since a generalist predator utilizes a variety of food sources to survive and shows prey-switching behavior at low focal prey density by reducing the predation pressure. On the other hand, the presence of Allee effect can potentially lead to a fairly complex prey–predator dynamics including the suppression of "the paradox of enrichment". In this paper, we explore the combined influence of reproductive Allee effect in prey growth and generalist predation on the resulting temporal as well as spatio-temporal dynamics. The temporal model mainly exhibits bistability in terms of stable equilibria. For the corresponding spatio-temporal model, we perform detailed theoretical analysis regarding the non-existence and existence of spatially heterogeneous steady states, and also provide conditions for Turing instability. The spatio-temporal model mainly exhibits stationary patterns and traveling wave solutions apart from the usual spatially homogeneous solutions. Our study reveals that oscillatory dynamics is less probable in the presence of abundant alternative food sources to predator population. [ABSTRACT FROM AUTHOR]