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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.

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]

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]

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]

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]

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]

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]

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]

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]

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]

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.

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]

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]

Dynamic regulation of the cellular proteome is mainly controlled in the endoplasmic reticulum (ER). Accumulation of misfolded proteins due to ER stress leads to the activation of unfolded protein response (UPR). The primary role of UPR is to reduce the bulk of damages and try to drive back the system to the former or a new homeostatic state by autophagy, while an excessive level of stress results in apoptosis. It has already been proven that the proper order and characteristic features of both surviving and self-killing mechanisms are controlled by negative and positive feedback loops, respectively. The new results suggest that these feedback loops are found not only within but also between branches of the UPR, fine-tuning the response to ER stress. In this review, we summarize the recent knowledge of the dynamical characteristic of endoplasmic reticulum stress response mechanism by using both theoretical and molecular biological techniques. In addition, this review pays special attention to describing the mechanism of action of the dynamical features of the feedback loops controlling cellular life-and-death decision upon ER stress. Since ER stress appears in diseases that are common worldwide, a more detailed understanding of the behaviour of the stress response is of medical importance. [ABSTRACT FROM AUTHOR]

A wireless monitoring system based on piezoelectric energy harvesting (PEH) is presented to provide fatigue data of wind turbine blades in operation. The system comprises three subsystems, each respectively providing the following functions: (i) the conversion of mechanical to electric energy by exploiting the bistable vibration of a composite beam with piezoelectric patches in post-buckling, (ii) harvesting the converted energy by means of a modified, commercial, off-the-shelf (COTS) circuit to feed a LiPo battery and (iii) the battery-powered acquisition and wireless transmission of sensory signals to the cloud to be elaborated upon by the end-user. The system was verified with ground tests under representative operation conditions, which demonstrated the fulfillment of the design requirements. The measurements indicated that the system provided 23% of the required power for fully autonomous operation when subjected to white noise base excitation of 1 g acceleration in the range of 1–20 Hz. [ABSTRACT FROM AUTHOR]

Bistability in spinal motoneurons supports tonic spike activity in the absence of excitatory drive. Earlier work in adult preparations suggested that smaller motoneurons innervating slow antigravity muscle fibers are more likely to generate bistability for postural maintenance. However, whether large motoneurons innervating fast-fatigable muscle fibers display bistability is still controversial. To address this, we examined the relationship between soma size and bistability in lumbar (L4–L5) ventrolateral α-motoneurons of choline acetyltransferase (ChAT)-green fluorescent protein (GFP) and Hb9-GFP mice during the first 4 wk of life. We found that as neuron size increases, the prevalence of bistability rises. Smaller α-motoneurons lack bistability, whereas larger fast α-motoneurons [matrix metalloproteinase-9 (MMP-9)+/Hb9+] with a soma area ≥ 400 µm2 exhibit significantly higher bistability. Ionic currents associated with bistability, including the persistent Nav1.6 current, the thermosensitive Trpm5 Ca2+-activated Na+ current, and the slowly inactivating Kv1.2 current, also scale with cell size. Serotonin evokes full bistability in large motoneurons with partial bistable properties but not in small motoneurons. Our study provides important insights into the neural mechanisms underlying bistability and how motoneuron size correlates with bistability in mice. NEW & NOTEWORTHY: Bistability is not a common feature of all mouse spinal motoneurons. It is absent in small, slow motoneurons but present in most large, fast motoneurons. This difference results from differential expression of ionic currents that enable bistability, which are highly expressed in large motoneurons but small or absent in small motoneurons. These results support a possible role for fast motoneurons in maintenance of tonic posture in addition to their known roles in fast movements. [ABSTRACT FROM AUTHOR]

Mapping neuronal activation using calcium imaging in vivo during behavioural tasks has advanced our understanding of nervous system function. In almost all of these studies, calcium imaging is used to infer spike probabilities because action potentials activate voltage‐gated calcium channels and increase intracellular calcium levels. However, neurons not only fire action potentials, but also convey information via intrinsic dynamics such as by generating bistable membrane potential states. Although a number of tools for spike inference have been developed and are currently being used, no tool exists for converting calcium imaging signals to maps of cellular state in bistable neurons. Purkinje neurons in the larval zebrafish cerebellum exhibit membrane potential bistability, firing either tonically or in bursts. Several studies have implicated the role of a population code in cerebellar function, with bistability adding an extra layer of complexity to this code. In the present study, we develop a tool, CaMLSort, which uses convolutional recurrent neural networks to classify calcium imaging traces as arising from either tonic or bursting cells. We validate this classifier using a number of different methods and find that it performs well on simulated event rasters as well as real biological data that it had not previously seen. Moreover, we find that CaMLsort generalizes to other bistable neurons, such as dopaminergic neurons in the ventral tegmental area of mice. Thus, this tool offers a new way of analysing calcium imaging data from bistable neurons to understand how they participate in network computation and natural behaviours. Key points: Calcium imaging, compriising the gold standard of inferring neuronal activity, does not report cellular state in neurons that are bistable, such as Purkinje neurons in the cerebellum of larval zebrafish. We model the relationship between Purkinje neuron electrical activity and its corresponding calcium signal to compile a dataset of state‐labelled simulated calcium signals.We apply machine‐learning methods to this dataset to develop a tool that can classify the state of a Purkinje neuron using only its calcium signal, which works well on real data even though it was trained only on simulated data.CaMLsort (Calcium imaging and Machine Learning based tool to sort intracellular state) also generalizes well to bistable neurons in a different brain region (ventral tegmental area) in a different model organism (mouse).This tool can facilitate our understanding of how these neurons carry out their functions in a circuit. [ABSTRACT FROM AUTHOR]

In this article, we have considered a planar slow–fast modified Leslie–Gower predator–prey model with a weak Allee effect in the predator, based on the natural assumption that the prey reproduces far more quickly than the predator. We present a thorough mathematical analysis demonstrating the existence of homoclinic orbits, heteroclinic orbits, singular Hopf bifurcation, canard limit cycles, relaxation oscillations, birth of canard explosion by combining the normal form theory of slow–fast systems, Fenichel's theorem and blow-up technique near non-hyperbolic point. We have obtained very rich dynamical phenomena of the model, including the saddle-node, Hopf, transcritical bifurcation, generalized Hopf, cusp point, homoclinic orbit, heteroclinic orbit, and Bogdanov–Takens bifurcations. Moreover, we have investigated the global stability of the unique positive equilibrium, as well as bistability, which shows that the system can display either "prey extinction", "stable coexistence", or "oscillating coexistence" depending on the initial population size and values of the system parameters. The theoretical findings are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper introduces an optimized orbit jump strategy for nonlinear vibration energy harvesters (VEHs). Nonlinear VEHs are a promising alternative to linear VEHs due to their broadband characteristics. However, they exhibit complex dynamical behaviors, including not only high-power inter-well orbits but also low-power intra-well orbits and chaos. The existence of low-power orbits in their dynamics can restrict their energy harvesting performance. In order to overcome this issue, this study investigates an orbit jump strategy that allows the VEH to transition from low-power intra-well orbits to high-power inter-well orbits. The orbit jump strategy, which is based on varying the buckling level of a bistable VEH, has been previously studied but not yet optimized. In this study, we optimize this orbit jump strategy to ensure practical reproducibility and robustness against variations in parameters or excitation. Through the combination of thorough experimental identification and high-performance computing of the complex transients during orbit jumps, we achieved high numerical accuracy in orbit jump modeling. This was possible by a developed Python CUDA code using GPU parallel computing to handle a large number of numerical resolutions of the nonlinear VEH model. These simulations facilitate the optimization of both the robustness and the energy cost of orbit jumps, based on a novel numerical criterion. Experimental tests were performed on a bistable VEH over a frequency range of 30 Hz, validating the numerical results obtained with the optimized orbit jump strategy. Experimental results show an average success rate of 48%, despite a variation of ± 15 % in the starting and ending times of the jump, leading to a robust and optimized orbit jump strategy. The proposed optimization procedure can be applied to other orbit jump strategies, and other types of nonlinear VEHs. The results indicate that the energy consumption required for a successful orbit jump ranges between 0.2 and 1 mJ, and can be restored within 0.2 s in the worst case. [ABSTRACT FROM AUTHOR]

Stratospheric dynamics are strongly affected by the absorption/emission of radiation in the Earth's atmosphere and Rossby waves that propagate upward from the troposphere, perturbing the zonal flow. Reduced order models of stratospheric wave–zonal interactions, which parameterize these effects, have been used to study interannual variability in stratospheric zonal winds and sudden stratospheric warming (SSW) events. These models are most sensitive to two main parameters: Λ , forcing the mean radiative zonal wind gradient, and h, a perturbation parameter representing the effect of Rossby waves. We take one such reduced order model with 20 years of ECMWF atmospheric reanalysis data and estimate Λ and h using both a particle filter and an ensemble smoother to investigate if the highly-simplified model can accurately reproduce the averaged reanalysis data and which parameter properties may be required to do so. We find that by allowing additional complexity via an unparameterized Λ (t) , the model output can closely match the reanalysis data while maintaining behavior consistent with the dynamical properties of the reduced-order model. Furthermore, our analysis shows physical signatures in the parameter estimates around known SSW events. This work provides a data-driven examination of these important parameters representing fundamental stratospheric processes through the lens and tractability of a reduced order model, shown to be physically representative of the relevant atmospheric dynamics. [ABSTRACT FROM AUTHOR]

Composite tape springs are curved shells with the ability to assume two energetically stable states. By carefully selecting layup and mold during manufacturing, these structures can store significant strain energy, making them ideal for deployable systems. Yet, their potential as reversible reconfigurable structures, particularly as adaptive hinges, remains largely unexplored. In structural applications, both stable states of these hinges must exhibit high stiffness to support loads while retaining the capacity for reversible reconfiguration. This paper introduces kinematics-based stacking concepts aimed at enhancing the stiffness of bistable hinges in both states, allowing for specific fold angles without compromising compliance. These designs leverage snap-through kinematics, resulting in unique architectures with customizable stiffness and stability. Additionally, the paper presents a novel energy-based semi-analytical approach for analyzing the stacking concepts. This approach involves constrained exploration of the energy landscape to assess the design space in terms of stiffness and energy barriers. Through comprehensive parametric studies, the research demonstrates significantly increased stiffness and reduced peak stresses compared to single tape spring designs. This research highlights the potential of employing tape springs as reconfigurable load-bearing structures in diverse applications, including precise adjustments of low-mass payloads like solar panels or antennas on space structures.

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.

Stratospheric dynamics are strongly affected by the absorption/emission of radiation in the Earth’s atmosphere and Rossby waves that propagate upward from the troposphere, perturbing the zonal flow. Reduced order models of stratospheric wave–zonal interactions, which parameterize these effects, have been used to study interannual variability in stratospheric zonal winds and sudden stratospheric warming (SSW) events. These models are most sensitive to two main parameters: Λ, forcing the mean radiative zonal wind gradient, and h, a perturbation parameter representing the effect of Rossby waves. We take one such reduced order model with 20 years of ECMWF atmospheric reanalysis data and estimate Λ and h using both a particle filter and an ensemble smoother to investigate if the highly-simplified model can accurately reproduce the averaged reanalysis data and which parameter properties may be required to do so. We find that by allowing additional complexity via an unparameterized Λ(t), the model output can closely match the reanalysis data while maintaining behavior consistent with the dynamical properties of the reduced-order model. Furthermore, our analysis shows physical signatures in the parameter estimates around known SSW events. This work provides a data-driven examination of these important parameters representing fundamental stratospheric processes through the lens and tractability of a reduced order model, shown to be physically representative of the relevant atmospheric dynamics.

The infectious disease caused by human immunodeficiency virus type 1 (HIV-1) remains a serious threat to human health. The current approach to HIV-1 treatment is based on the use of highly active antiretroviral therapy, which has side effects and is costly. For clinical practice, it is highly important to create functional cures that can enhance immune control of viral growth and infection of target cells with a subsequent reduction in viral load and restoration of the immune status. HIV-1 control efforts with reliance on immunotherapy remain at a conceptual stage due to the complexity of a set of processes that regulate the dynamics of infection and immune response. For this reason, it is extremely important to use methods of mathematical modeling of HIV-1 infection dynamics for theoretical analysis of possibilities of reducing the viral load by affecting the immune system without the usage of antiviral therapy. The aim of our study is to examine the existence of bi-, multistability and hysteresis properties with a meaningful mathematical model of HIV-1 infection. The model describes the most important blocks of the processes of interaction between viruses and the human body, namely, the spread of infection in productively and latently infected cells, the appearance of viral mutants and the development of the T cell immune response. Furthermore, our analysis aims to study the possibilities of transferring the clinical pattern of the disease from a more severe state to a milder one. We analyze numerically the conditions for the existence of steady states of the mathematical model of HIV-1 infection for the numerical values of model parameters corresponding to phenotypically different variants of the infectious disease course. To this end, original computational methods of bifurcation analysis of mathematical models formulated with systems of ordinary differential equations and delay differential equations are used. The macrophage activation rate constant is considered as a bifurcation parameter. The regions in the model parameter space, in particular, for the rate of activation of innate immune cells (macrophages), in which the properties of bi-, multistability and hysteresis are expressed, have been identified, and the features cha rac terizing transition kinetics between stable equilibrium states have been explored. Overall, the results of bifurcation analysis of the HIV-1 infection model form a theoretical basis for the development of combination immune-based therapeutic approaches to HIV-1 treatment. In particular, the results of the study of the HIV-1 infection model for parameter sets corresponding to different phenotypes of disease dynamics (typical, long-term non-progressing and rapidly progressing courses) indicate that an effective functional treatment (cure) of HIV-1-infected patients requires the development of a personalized approach that takes into account both the properties of the HIV-1 quasispecies population and the patient’s immune status.

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.

A design concept is proposed for the building block, a dot, of programmable braille readers utilizing bistable shell buckling, magnetic actuation, and pneumatic loading. The design process is guided by Finite Element simulations, which are initially validated through precision experiments conducted on a scaled‐up, single‐shell model system. Then, the simulations are leveraged to systematically explore the design space, adhering to the standardized geometric and physical specifications of braille systems. The findings demonstrate the feasibility of selecting design parameters that satisfy both geometric requirements and blocking forces under moderate magnetic fields, facilitated by pneumatic loading to switch between the two stable states. While the study is focused on experimentally validated numerical simulations, it is also identify several manufacturing challenges that need to be resolved for future physical implementations. [ABSTRACT FROM AUTHOR]

To reduce the chance of predation, many prey species adopt group defense mechanisms. While it is commonly believed that such defense mechanisms lead to positive feedback on prey density, a closer observation reveals that it may impact the growth rate of species. This is because individuals invest more time and effort in defense rather than reproductive activities. In this study, we delve into a predator–prey system where predator-induced fear influences the birth rate of prey, and the prey species exhibit group defense mechanism. We adopt a nonmonotonic functional response to govern the predator–prey interaction, which effectively captures the group defense mechanism. We present a detailed mathematical analysis, encompassing the determination of feasible equilibria and their stability conditions. Through the analytical approach, we demonstrate the occurrence of Hopf and Bogdanov–Takens (BT) bifurcations. We observe two distinct types of bistabilities in the system: one between interior and predator-free equilibria, and another between limit cycle and predator-free equilibrium. Our findings reveal that the parameters associated with group defense and predator-induced fear play significant roles in the survival and extinction of populations. [ABSTRACT FROM AUTHOR]

The mammalian cell cycle alternates between two phases - S-G2-M with high levels of A- and B-type cyclins (CycA and CycB, respectively) bound to cyclin-dependent kinases (CDKs), and G1 with persistent degradation of CycA and CycB by an activated anaphase promoting complex/cyclosome (APC/C) bound to Cdh1 (also known as FZR1 in mammals; denoted APC/C:Cdh1). Because CDKs phosphorylate and inactivate Cdh1, these two phases are mutually exclusive. This 'toggle switch' is flipped from G1 to S by cyclin-E bound to a CDK (CycE:CDK), which is not degraded by APC/C:Cdh1, and from M to G1 by Cdc20-bound APC/C (APC/C:Cdc20), which is not inactivated by CycA:CDK or CycB:CDK. After flipping the switch, cyclin E is degraded and APC/C:Cdc20 is inactivated. Combining mathematical modelling with single-cell timelapse imaging, we show that dysregulation of CycB:CDK disrupts strict alternation of the G1-S and M-G1 switches. Inhibition of CycB:CDK results in Cdc20-independent Cdh1 'endocycles', and sustained activity of CycB:CDK drives Cdh1-independent Cdc20 endocycles. Our model provides a mechanistic explanation for how wholegenome doubling can arise, a common event in tumorigenesis that can drive tumour evolution. [ABSTRACT FROM AUTHOR]