Mean Switching Time Research Articles

Directional switching behavior of swarming systems with social and nonlinear interactions

Coordinated directional switching can occur among members of many mobile biological communities. Some studies show that self-propelled particle models can describe the directional switching behavior well. The key to understanding group movement is to determine the influential factors relevant to directional switching behavior. This paper focuses on the impact of social and nonlinear interactions on the directional switching behavior observed in swarming systems. In which, the nonlinear interaction is represented as a function of a trade-off between the velocity and velocity direction of its neighbors. Based on the framework of dimension reduction theory, the high-dimensional complex model is simplified into a one-dimensional simple model, and the stationary probability density and mean switching time are obtained by theoretical analysis of the one-dimensional model. It can be seen that social and nonlinear interactions play an important role in regulating the directional switching behaviors of swarming systems. Specifically, the increase of group density and nonlinear parameter can inhibit the directional switches. For Erdös-Rényi networks, the large mean degree can suppress the directional switching behavior. For scale-free networks, increasing the degree heterogeneity can reduce the mean switching time. The results reveal the underlying mechanisms by which social and nonlinear interactions influence the directional switching behaviors of swarming systems, and provide a theoretical foundation for the design of bio-inspired devices with specific functions.

Compartmental exchange regulates steady states and stochastic switching of a phosphorylation network

The phosphoregulation of proteins with multiple phosphorylation sites is governed by biochemical reaction networks that can exhibit multistable behavior. However, the behavior of such networks is typically studied in a single reaction volume, while cells are spatially organized into compartments that can exchange proteins. In this work, we use stochastic simulations to study the impact of compartmentalization on a two-site phosphorylation network. We characterize steady states and fluctuation-driven transitions between them as a function of the rate of protein exchange between two compartments. Surprisingly, the average time spent in a state before stochastically switching to another depends nonmonotonically on the protein exchange rate, with the most frequent switching occurring at intermediate exchange rates. At sufficiently small exchange rates, the state of the system and mean switching time are controlled largely by fluctuations in the balance of enzymes in each compartment. This leads to negatively correlated states in the compartments. For large exchange rates, the two compartments behave as a single effective compartment. However, when the compartmental volumes are unequal, the behavior differs from a single compartment with the same total volume. These results demonstrate that exchange of proteins between distinct compartments can regulate the emergent behavior of a common signaling motif.

Directional switches in network-organized swarming systems with delay.

Coordinated directional switches can emerge between members of moving biological groups. Previous studies have shown that the self-propelled particles model can well reproduce directional switching behaviors, but it neglects the impact of social interactions. Thus, we focus on the influence of social interactions on the ordered directional switching motion of swarming systems, in which homogeneous Erdös-Rényi networks, heterogeneous scale-free networks, networks with community structures, and real-world animal social networks have been considered. The theoretical estimation of mean switching time is obtained, and the results show that the interplay between social and delayed interactions plays an important role in regulating directional switching behavior. To be specific, for homogeneous Erdös-Rényi networks, the increase in mean degree may suppress the directional switching behaviors if the delay is sufficiently small. However, when the delay is large, the large mean degree may promote the directional switching behavior. For heterogeneous scale-free networks, the increase of degree heterogeneity can reduce the mean switching time if the delay is sufficiently small, while the increasing degree heterogeneity may suppress the ordered directional switches if the delay is large. For networks with community structures, higher communities can promote directional switches for small delays, while for large delays, it may inhibit directional switching behavior. For dolphin social networks, delay can promote the directional switching behavior. Our results bring to light the role of social and delayed interactions in the ordered directional switching motion.

Noise induced bistability in a fluctuating environment

Bistability in some systems does not occur at the mean-field level but is induced by noise. In this work, we consider a system which exhibits bistability induced by noise but in the presence of environmental fluctuations. The system can transition between two environmental states at a specified rate. It has absorbing boundaries in one state and can switch between two metastable states in the other. At small values of a system parameter (ϵ), the model exhibits noise-induced switching behaviour and the probability distribution is bimodal which becomes unimodal at large values of ϵ. We calculate the exact eigenvalues and steady-state solutions of the system. We further extend the investigation by calculating the mean switching time between the two metastable states in the small parameter limit and compare its accuracy with simulation results.

Mathematical analysis of the limiting behaviors of a chromatin modification circuit

In the last decade, the interactions among histone modifications and DNA methylation and their effect on the DNA structure, i.e., chromatin state, have been identified as key mediators for the maintenance of cell identity, defined as epigenetic cell memory. In this paper, we determine how the positive feedback loops generated by the auto- and cross-catalysis among repressive modifications affect the temporal duration of the cell identity. To this end, we conduct a stochastic analysis of a recently published chromatin modification circuit considering two limiting behaviors: fast erasure rate of repressive histone modifications or fast erasure rate of DNA methylation. In order to perform this mathematical analysis, we first show that the deterministic model of the system is a singular singularly perturbed (SSP) system and use a model reduction approach for SSP systems to obtain a reduced one-dimensional model. We thus analytically evaluate the reduced system’s stationary probability distribution and the mean switching time between active and repressed chromatin states. We then add a computational study of the original reaction model to validate and extend the analytical findings. Our results show that the absence of DNA methylation reduces the bias of the system’s stationary probability distribution toward the repressed chromatin state and the temporal duration of this state’s memory. In the absence of repressive histone modifications, we also observe that the time needed to reactivate a repressed gene with an activating input is less stochastic, suggesting that repressive histone modifications specifically contribute to the highly variable latency of state reactivation.

Delay-induced directional switches and mean switching time in swarming systems

Coordinated directional switches often emerge in moving biological groups replete with individual-level interactions. Recent self-propelled particles models can somewhat mimic the patterns of directional switches, but they usually do not include the effects of time delays in the interactions. Here, we focus on investigating the influence of time-delay interactions on the collective motion of swarming locusts, an experimentally well-studied system that exhibits ordered switches between clockwise and counterclockwise movement. We show, both analytically and numerically, that time delays of different types can affect the directional switches. Specifically, for the sufficiently small response delay, increasing the transmission delay can increase the mean switching time, while, for the large response delay, increasing the transmission delay may destroy the ordered directional switches. Our results decipher the role of time-delay interactions in the collective motion, which could be beneficial to the design of collective intelligent devices.

Stochastic switches of eutrophication and oligotrophication: Modeling extreme weather via non-Gaussian Lévy noise.

Disturbances related to extreme weather events, such as hurricanes, heavy precipitation events, and droughts, are important drivers of evolution processes of a shallow lake ecosystem. A non-Gaussian α-stable Lévy process is esteemed to be the most suitable model to describe such extreme events. This paper incorporates extreme weather via α-stable Lévy noise into a parameterized lake model for phosphorus dynamics. We obtain the stationary probability density function of phosphorus concentration and examine the pivotal roles of α-stable Lévy noise on phosphorus dynamics. The switches between the oligotrophic state and the eutrophic state can be induced by the noise intensity σ, skewness parameter β, or stability index α. We calculate the mean first passage time, also referred to as the mean switching time, from the oligotrophic state to the eutrophic state. We observe that the increased noise intensity, skewness parameter, or stability index makes the mean switching time shorter and thus accelerates the switching process and facilitates lake eutrophication. When the frequency of extreme weather events exceeds a critical value, the intensity of extreme events becomes the most key factor for promoting lake eutrophication. As an application, we analyze the available data of Lake Taihu (2014-2018) for monthly precipitation, phosphorus, and chlorophyll-a concentrations and quantify the linkage among them using the Lévy-stable distribution. This study provides a fundamental framework to uncover the impact of any extreme climate event on aquatic nutrient status.

Josephson-junction-based axion detection through resonant activation

We discuss the resonant activation phenomenon on a Josephson junction due to the coupling of the Josephson system with axions. We show how such an effect can be exploited for axion detection. A nonmonotonic behavior, with a minimum, of the mean switching time from the superconducting to the resistive state versus the ratio of the axion energy and the Josephson plasma energy is found. We demonstrate how variations in switching times make it possible to detect the presence of the axion field. An experimental protocol for observing axions through their coupling with a Josephson system is proposed.

Effect of phase disturbance on logical vibrational resonance

Logical vibrational resonance (LVR), which can be considered as a potential mechanism for designing new-style logic devices, attracts more and more attention. However, phase disturbance has not yet been considered in the related studies. However, tiny phase disturbance can be induced by some factors. Here stochastic phase disturbance is modeled by Wiener process. Through calculating successful probability and mean switching time, we demonstrate that (1) comparing with no phase disturbance or relatively large phase disturbance, tiny phase disturbance in the high-frequency driving force destroys the reliability and reduces the response speed of logic devices, depending on amplitude and frequency of driving force; (2) frequency ratio between two driving forces significantly affects the performance of logic devices, and large frequency ratio may let logic system deteriorate very quickly. Finally, the intuitive interpretation for the effect of phase disturbance is given based on the motion of the coupled Brownian particles in potential wells.

Lévy noise effects on Josephson junctions

We review three different approaches to investigate the non-equilibrium stochastic dynamics of a Josephson junction affected by Lévy-distributed current fluctuations. First, we study the lifetime in the metastable superconducting state of current-biased short and long junctions, in the presence of Gaussian and Lévy noise sources. We highlight the noise-induced nonmonotonic behavior of the mean switching time as a function of noise intensity and driving frequency, that is the noise enhanced stability and the stochastic resonant activation, respectively. Then, we characterize the Lévy noise source through the average voltage drop across a current-biased junction. The voltage measurement versus the noise intensity allows to infer the value of the stability index that characterizes Lévy-distributed fluctuations. The numerical calculation of the average voltage drop across the junction well agrees with the analytical estimate of the average velocity for Lévy-driven escape processes from a metastable state. Finally, we look at the distribution of switching currents out of the zero-voltage state, when a Lévy noise signal is added to a linearly ramped bias current. The analysis of the cumulative distribution function of the switching currents gives information on both the Lévy stability index and the intensity of fluctuations. We present also a theoretical model to catch the features of the Lévy signal from a measured distribution of switching currents. The phenomena discussed in this work can pave the way for an effective and reliable Josephson-based scheme to characterize Lévy components eventually embedded in an unknown noisy signal.

Coordinating directional switches in pigeon flocks: the role of nonlinear interactions

The mechanisms inducing unpredictably directional switches in collective and moving biological entities are largely unclear. Deeply understanding such mechanisms is beneficial to delicate design of biologically inspired devices with particular functions. Here, articulating a framework that integrates data-driven, analytical and numerical methods, we investigate the underlying mechanism governing the coordinated rotational flight of pigeon flocks with unpredictably directional switches. Particularly using the sparse Bayesian learning method, we extract the inter-agent interactional dynamics from the high-resolution GPS data of three pigeon flocks, which reveals that the decision-making process in rotational switching flight performs in a more nonlinear manner than in smooth coordinated flight. To elaborate the principle of this nonlinearity of interactions, we establish a data-driven particle model with two potential wells and estimate the mean switching time of rotational direction. Our model with its analytical and numerical results renders the directional switches of moving biological groups more interpretable and predictable. Actually, an appropriate combination of natures, including high density, stronger nonlinearity in interactions, and moderate strength of noise, can enhance such highly ordered, less frequent switches.

Resonant response drives sensitivity of Josephson escape detector

The Josephson junction as a switching detector of weak signals is investigated in presence of noise in the frame of rotating pendulum model. The parameter range, where the detection can be more efficient, is found. It has been demonstrated, that with decrease of the signal power the double minima of the mean switching time and the standard deviation are transformed into a single minimum, which corresponds to interplay between noise suppression and resonant activation regimes. The resonant nature of escape allows to detect weak signals, whose amplitudes are weaker than the difference between critical current and bias current of a Josephson junction. With decrease of damping an efficient detection becomes possible even at subharmonics of the resonance frequency.

Which cognitive functions subserve clustering and switching in category fluency? Generalisations from an extended set of semantic categories using linear mixed-effects modelling.

Clustering and switching are hypothesised to reflect the automatic and controlled components in category fluency, respectively, but how they are associated with cognitive functions has not been fully elucidated, due to several uncertainties. (1) The conventional scoring method that segregates responses by semantic categories could not optimally dissociate the automatic and controlled components. (2) The temporal structure of individual responses, as characterised by mean retrieval time (MRT) and mean switching time (MST), has seldom been analysed alongside the more well-studied variables, cluster size (CS) and number of switches (NS). (3) Most studies examined only one to a few semantic categories, raising concerns of generalisability. This study built upon a distance-based automatic clustering procedure, referred to as temporal-semantic distance procedure, to thoroughly characterise the category fluency performance. Linear mixed-effects (LME) modelling was applied to re-examine the differential associations of clustering and switching with cognitive functions with a sample of 80 university students. Our results revealed that although lexical retrieval speed (LRS) is clearly the determining factor for effective clustering and switching, matrix reasoning and processing speed also have significant roles to play, possibly in the processes of identifying and validating the semantic relationships. Interestingly, total fluency score was accurately predicted by the four clustering/switching indices alone; including the cognitive variables did not significantly improve the prediction. These findings underline the importance of the clustering and switching indices in explaining the category fluency performance and the cognitive demands in category fluency.

Periodic and aperiodic force-induced logical stochastic resonance in a bistable system.

It was demonstrated recently that there are optimal windows of noise intensity or frequency and amplitude of the periodic driving force, which let a bistable system operate reliably as logic gates. These phenomena are called logical stochastic resonance (LSR). Given that the driving force is not always perfect regular, there may be phase disturbance in driving force; therefore, the Wiener process is used here to model phase disturbance of driving force, and then the effects of phase disturbance on reliability and agility of logic gates are explored in detail. Comparing with the periodic force, the aperiodic force with appropriate intensity phase disturbance can drive a bistable system to yield phenomena similar to LSR in a wider reliable region and can reduce mean switching time to obtain a faster response of logic devices to the input signal. On the other hand, depending on the amplitude and average angular frequency, moderate-intensity phase disturbance may also reduce success probability and increase mean switching time and thus lead to the instability and the slower response of logic devices.

Mathematical analysis for stochastic model of Alzheimer’s disease

Alzheimer’s disease is a worldwide disease of dementia and is characterized by beta-amyloid plaques. Increasing evidences show that there is a positive feedback loop between the level of beta-amyloid and the level of calcium. In this paper, stochastic noises are incorporated into a minimal model of Alzheimer’s disease which focuses upon the evolution of beta-amyloid and calcium. Mathematical analysis indicates that solutions of the model without stochastic noises converge either to a unique equilibrium or to bistable equilibria. Analytical conditions for the stochastic P-bifurcation are derived by means of technique of slow-fast dynamical systems. A formula is presented to approximate the mean switching time from a normal state to a pathological state. A disease index is also proposed to predict the risk to transit from a normal state to a disease state. Further numerical simulations reveal how the parameters influence the evolutionary outcomes of beta-amyloid and calcium. These results give new insights on the strategies to slow the development of Alzheimer’s disease.

Suppression of switching errors in weakly damped Josephson junctions

The task of the Josephson junction switching is numerically solved in the framework of the classical RCSJ model with white Gaussian noise. In order to switch the junction to the resistive state a periodic supra-threshold signal is applied. The operational mode is similar to the single photon counter proposed earlier. Here we consider a purely classical situation in order to find out how far the typical aluminium Josephson junction is from the single photon operational mode. We have found that for the considered parameters, if the switching happens due to external periodic signal, it occurs mostly during the first two periods of driving, and the number of photons, needed for switching, is more than one hundred. Also we observe the double minima of the mean switching time and the standard deviation versus the driving frequency. This determines the parameter range, optimal for reliable switching, which can be used as a guidance in quasi-classical and quantum approaches.

Reduced thermal stability of antiferromagnetic nanostructures

Antiferromagnetic materials hold promising prospects in novel types of spintronics applications. Assessing the stability of antiferromagnetic nanostructures against thermal excitations is a crucial aspect of designing devices with a high information density. Here we use theoretical calculations and numerical simulations to determine the mean switching time of antiferromagnetic nanoparticles in the superparamagnetic limit. It is demonstrated that the thermal stability is drastically reduced compared to ferromagnetic particles in the limit of low Gilbert damping, attributed to the exchange enhancement of the attempt frequencies. It is discussed how the system parameters have to be engineered in order to optimize the switching rates in antiferromagnetic nanoparticles.

Consensus and diversity in multistate noisy voter models.

We study a variant of the voter model with multiple opinions; individuals can imitate each other and also change their opinion randomly in mutation events. We focus on the case of a population with all-to-all interaction. A noise-driven transition between regimes with multimodal and unimodal stationary distributions is observed. In the former, the population is mostly in consensus states; in the latter, opinions are mixed. We derive an effective death-birth process, describing the dynamics from the perspective of one of the opinions and use it to analytically compute marginals of the stationary distribution. These calculations are exact for models with homogeneous imitation and mutation rates and an approximation if rates are heterogeneous. Our approach can be used to characterize the noise-driven transition and to obtain mean switching times between consensus states.

Using control to shape stochastic escape and switching dynamics.

We present a strategy to control the mean stochastic switching times of general dynamical systems with multiple equilibrium states subject to Gaussian white noise. The control can either enhance or abate the probability of escape from the deterministic region of attraction of a stable equilibrium in the presence of external noise. We synthesize a feedback control strategy that actively changes the system's mean stochastic switching behavior based on the system's distance to the boundary of the attracting region. With the proposed controller, we are able to achieve a desired mean switching time, even when the strength of noise in the system is not known. The control method is analytically validated using a one-dimensional system, and its effectiveness is numerically demonstrated for a set of dynamical systems of practical importance.

Scaling properties of noise-induced switching in a bistable tunnel diode circuit

Noise-induced switching between coexisting metastable states occurs in a wide range of far-from-equilibrium systems including micro-mechanical oscillators, epidemiological and climate change models, and nonlinear electronic transport in tunneling structures such as semiconductor superlattices and tunnel diodes. In the case of tunnel diode circuits, noise-induced switching behavior is associated with negative differential resistance in the static current-voltage characteristics and bistability, i.e., the existence of two macroscopic current states for a given applied voltage. Noise effects are particularly strong near the onset and offset of bistable current behavior, corresponding to bifurcation points in the associated dynamical system. In this paper, we show that the tunnel diode system provides an excellent experimental platform for the precision measurement of scaling properties of mean switching times versus applied voltage near bifurcation points. More specifically, experimental data confirm that the mean switching time scales logarithmically as the 3/2 power of voltage difference over an exceptionally wide range of time scales and noise intensities.