Noise-induced Transitions Research Articles

Run-and-tumble motion of ellipsoidal microswimmers

A hallmark of bacteria is their so-called “run-and-tumble” motion and its variants, consisting of a sequence of linear directed “runs” and distinct rotation events that constantly alternate due to biochemical feedback. It plays a crucial role in the ability of bacteria to move through chemical gradients and has inspired a fundamental active particle model. Nevertheless, synthetic active particles generally do not exhibit run-and-tumble motion but rather active Brownian motion. We show in experiments that ellipsoidal thermophoretic Janus particles, propelling along their short axis, can yield run-and-reverse motion, i.e., where rotation events flip the direction of motion, even without feedback. Their hydrodynamic wall interactions under strong confinement give rise to an effective double-well potential for the declination of the short axis. The geometry-induced timescale separation of the in-plane rotational dynamics and noise-induced transitions in the potential then yield run-and-reverse motion. Published by the American Physical Society 2024

The effect of diffusion on multistability and stochastic sensitivity in spatially extended systems

A spatially-extended reaction-diffusion model is considered. The work is focused on self-organization mechanisms of diffusion instability and Turing pattern formation. Pattern generation and multistability of the system is demonstrated for varying diffusion intensity. In the stochastic variant of the model, the sensitivity of coexisting patterns to noise is studied. The stochastic sensitivity function technique is used for the analysis of noise-induced transitions between patterns. Application of stochastic sensitivity functions is discussed on examples.

Bifurcation analysis and exploration of noise-induced transitions of a food chain model with Allee effect

Seeking shelter from threats is a widespread instinct across species, specially employed by prey to avoid direct confrontations with predators. The present investigation centers on a three-species food chain model wherein the basal prey, characterized by logistic growth, seeks refuge to evade the intermediate predator, while the intermediate predator, in turn, seeks refuge to avoid encounters with the top predator. Additionally, our model assumes that the presence of the top predator induces a mate-finding Allee effect among the intermediate predator. We investigate how varying levels of refuge, along with other critical parameters such as the reproduction rate of the basal prey and the natural mortality rate of the top predator, influence system’s dynamics within the biparametric planes. Our model displays multistability and undergoes transcritical, saddle–node, Bogdanov–Takens and cusp bifurcations across different parameters. Moreover, the external environmental noise can induce interesting dynamics in the predator–prey system, resulting in noise-induced frequent transitions between distinct interior attractors or from interior to axial attractors. This phenomenon is particularly notable in scenarios where the deterministic model exhibits tristability. In summary, our findings offer potential new avenues for developing control strategies within the realm of community ecology in constant as well as fluctuating environments.

Noise-induced phase transitions in hybrid quantum circuits

Noise-induced phase transitions in hybrid quantum circuits

Learning noise-induced transitions by multi-scaling reservoir computing

Noise is usually regarded as adversarial to extracting effective dynamics from time series, such that conventional approaches usually aim at learning dynamics by mitigating the noisy effect. However, noise can have a functional role in driving transitions between stable states underlying many stochastic dynamics. We find that leveraging a machine learning model, reservoir computing, can learn noise-induced transitions. We propose a concise training protocol with a focus on a pivotal hyperparameter controlling the time scale. The approach is widely applicable, including a bistable system with white noise or colored noise, where it generates accurate statistics of transition time for white noise and specific transition time for colored noise. Instead, the conventional approaches such as SINDy and the recurrent neural network do not faithfully capture stochastic transitions even for the case of white noise. The present approach is also aware of asymmetry of the bistable potential, rotational dynamics caused by non-detailed balance, and transitions in multi-stable systems. For the experimental data of protein folding, it learns statistics of transition time between folded states, enabling us to characterize transition dynamics from a small dataset. The results portend the exploration of extending the prevailing approaches in learning dynamics from noisy time series.

Machine learning for the identification of phase transitions in interacting agent-based systems: A Desai-Zwanzig example.

Deriving closed-form analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM-the Desai-Zwanzig model-in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and we show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates that facilitates, in our example, the identification of a single parameter-dependent ordinary differential equation(ODE) in these coordinates. We identify this ODE through a residual neural network inspired by a numerical integration scheme (forward Euler). We then use the identified ODE-enabled through an odd symmetry transformation-to construct the bifurcation diagram exhibiting the phase transition.

Noise-induced phase transition in the Vicsek model through eigen microstate methodology

Abstract This paper presents a comprehensive framework for analyzing phase transitions in collective models like the Vicsek model under various noise types. The Vicsek model, focuses on understanding the collective behaviors of social animals, is known for its discontinuous phase transitions under vector noise. However, its behavior under scalar noise remains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and non-equilibrium state, the eigen microstate method is employed here for a quantitative examination of the phase transitions in the Vicsek model under both vector and scalar noise. The study finds that the Vicsek model exhibits discontinuous phase transitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for these phase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions with the escalation of population density.

Modeling correlated uncertainties in stochastic compartmental models

We consider compartmental models of communicable disease with uncertain contact rates. Stochastic fluctuations are often added to the contact rate to account for uncertainties. White noise, which is the typical choice for the fluctuations, leads to significant underestimation of the disease severity. Here, starting from reasonable assumptions on the social behavior of individuals, we model the contacts as a Markov process which takes into account the temporal correlations present in human social activities. Consequently, we show that the mean-reverting Ornstein–Uhlenbeck (OU) process is the correct model for the stochastic contact rate. We demonstrate the implication of our model on two examples: a Susceptibles–Infected–Susceptibles (SIS) model and a Susceptibles–Exposed–Infected–Removed (SEIR) model of the COVID-19 pandemic and compare the results to the available US data from the Johns Hopkins University database. In particular, we observe that both compartmental models with white noise uncertainties undergo transitions that lead to the systematic underestimation of the spread of the disease. In contrast, modeling the contact rate with the OU process significantly hinders such unrealistic noise-induced transitions. For the SIS model, we derive its stationary probability density analytically, for both white and correlated noise. This allows us to give a complete description of the model’s asymptotic behavior as a function of its bifurcation parameters, i.e., the basic reproduction number, noise intensity, and correlation time. For the SEIR model, where the probability density is not available in closed form, we study the transitions using Monte Carlo simulations. Our modeling approach can be used to quantify uncertain parameters in a broad range of biological systems.

Noise-induced transitions past the onset of a steady symmetry-breaking bifurcation: The case of the sudden expansion

Noise-induced transitions past the onset of a steady symmetry-breaking bifurcation: The case of the sudden expansion

Field-theoretic approach to neutron noise in nuclear reactors.

An operating nuclear reactor is designed to maintain a sustained fission chain reaction in its core, which results from a delicate balance between neutron creations (i.e., fissions) and total absorptions. This balance is associated with random fluctuations that can have two, very different, origins. A distinction must thus be made between low-power noise, whose origin lies in the inherently stochastic nature of neutron interactions with matter, and high-power noise, whose origin lies in the particular thermomechanical constraints associated with the environment in which neutrons propagate. Modeling the behavior of this noisy neutron population with the help of stochastic differential equations, we first show how the Martin-Siggia-Rose-Janssen-De Dominicis (MSRJD) formalism, providing a field theoretical representation of the problem, reveals a convenient and adapted tool for the calculation of observable consequences of neutron noise. In particular, we show how the MSRJD approach is capable of encompassing both types of neutron noises in the same formalism. Emphasizing then on power noise, it is shown how the self-sustained chain reaction developing in a reactor core might be sensitive to noise-induced transitions. Establishing an unprecedented connection between the neutron population evolving in a reactor core and the celebrated Kardar-Parisi-Zhang (KPZ) equation, we indeed find evidence that a noisy reactor core power distribution might be subject to a process analogous to the roughening transition, well-known to occur in systems described by the KPZ equation.

A robust ultrasensitive transcriptional switch in noisy cellular environments

Ultrasensitive transcriptional switches enable sharp transitions between transcriptional on and off states and are essential for cells to respond to environmental cues with high fidelity. However, conventional switches, which rely on direct repressor-DNA binding, are extremely noise-sensitive, leading to unintended changes in gene expression. Here, through model simulations and analysis, we discovered that an alternative design combining three indirect transcriptional repression mechanisms, sequestration, blocking, and displacement, can generate a noise-resilient ultrasensitive switch. Although sequestration alone can generate an ultrasensitive switch, it remains sensitive to noise because the unintended transcriptional state induced by noise persists for long periods. However, by jointly utilizing blocking and displacement, these noise-induced transitions can be rapidly restored to the original transcriptional state. Because this transcriptional switch is effective in noisy cellular contexts, it goes beyond previous synthetic transcriptional switches, making it particularly valuable for robust synthetic system design. Our findings also provide insights into the evolution of robust ultrasensitive switches in cells. Specifically, the concurrent use of seemingly redundant indirect repression mechanisms in diverse biological systems appears to be a strategy to achieve noise-resilience of ultrasensitive switches.

Noise-induced transitions in an avian influenza model with the Allee effect

This paper presents noise-induced transitions in a stochastic avian influenza model with Allee effect. In the deterministic case, one of three disease-free equilibria is always globally asymptotically stable in its attractive domain, and there is a unique endemic equilibrium when the basic reproduction number R_{0}>1. In the stochastic case, a new dynamic phenomenon of noise-induced transition can be observed, that is, the stochastic trajectory can exit from the neighborhood of the epidemic equilibrium and pass into the vicinity of the trivial equilibrium. More precisely, in this paper, based on the stochastic sensitivity function technique, we construct the confidence ellipse and then estimate the critical value of the noise intensity leading to extinction. We also propose useful control strategies to prevent the noise-induced extinction.

Probabilistic computing with NbOx metal-insulator transition-based self-oscillatory pbit

Energy-based computing is a promising approach for addressing the rising demand for solving NP-hard problems across diverse domains, including logistics, artificial intelligence, cryptography, and optimization. Probabilistic computing utilizing pbits, which can be manufactured using the semiconductor process and seamlessly integrated with conventional processing units, stands out as an efficient candidate to meet these demands. Here, we propose a novel pbit unit using an NbOx volatile memristor-based oscillator capable of generating probabilistic bits in a self-clocking manner. The noise-induced metal-insulator transition causes the probabilistic behavior, which can be effectively modeled using a multi-noise-induced stochastic process around the metal-insulator transition temperature. We demonstrate a memristive Boltzmann machine based on our proposed pbit and validate its feasibility by solving NP-hard problems. Furthermore, we propose a streamlined operation methodology that considers the autocorrelation of individual bits, enabling energy-efficient and high-performance probabilistic computing.

Partisan voter model: Stochastic description and noise-induced transitions.

We give a comprehensive mean-field analysis of the partisan voter model (PVM) and report analytical results for exit probabilities, fixation times, and the quasistationary distribution. In addition, and similarly to the noisy voter model, we introduce a noisy version of the PVM, named the noisy partisan voter model (NPVM), which accounts for the preferences of each agent for the two possible states, as well as for idiosyncratic spontaneous changes of state. We find that the finite-size noise-induced transition of the noisy voter model is modified in the NPVM leading to the emergence of intermediate phases that were absent in the standard version of the noisy voter model, as well as to both continuous and discontinuous transitions.

Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger

Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger

A generalist predator–prey system with the effects of fear and refuge in deterministic and stochastic environments

In the present study, we investigate the dynamics of a generalist predator–prey system by considering that the fear of predators suppresses the birth rate and enhances the intraspecies competition of the prey species. Also, we assume that a constant proportion of the prey population is taking refuge, which results in a reduction in the predation pressure. We consider Cosner functional response to describe the interactions between prey and predator species. We rigorously analyze the proposed model analytically as well as numerically. We see that the system exhibits multi-stable configurations under identical ecological conditions by allowing different bifurcation scenarios, including saddle–node, Hopf and transcritical bifurcations with varying degrees of fear, on the prey’s reproduction and intraspecies competition, induced by the predator species. The emergence of multistability scenarios in the system is also stimulated by the birth rate of prey species and the growth in predator species due to the additional food sources. We modify our proposed model to its stochastic counterpart by considering the impact of environmental white noises on the natural death rates of both prey and predator species. The simulation results for the stochastic system demonstrate that the fluctuations in the densities of prey and predator populations due to stochastic perturbations are highly sensitive to the intensities of the environmental noises. Additionally, we find that the stochastic system showcases noise-induced transitions whenever the deterministic system exhibits bistability.

Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity

It is universally accepted that noise may bring order to complex nonequilibrium systems. Most strikingly, entirely new states not seen in the noiseless system can be induced purely by including multiplicative noise-an effect known as pure noise-induced transitions. It was first observed in superfluids in the 1980s. Recent results in complex nonequilibrium systems have also shown how new collective states emerge from such pure noise-induced transitions, such as the foraging behavior of insect colonies, and schooling in fish. Here we report such effects of noise in a quantum-mechanical system without a classical limit. We use a minimal model of a nonlinearly damped oscillator in a fluctuating environment that is analytically tractable, and whose microscopic physics can be understood. When multiplicative environmental noise is included, the system is seen to transition to a limit-cycle state. The noise-induced quantum limit cycle also exhibits other genuinely nonclassical traits, such as Wigner negativity and number-parity sensitive circulation in phase space. Such quantum limit cycles are also conservative. These properties are in stark contrast to those of a widely used limit cycle in the literature, which is dissipative and loses all Wigner negativity. Our results establish the existence of a pure noise-induced transition that is nonclassical and unique to open quantum systems. They illustrate a fundamental difference between quantum and classical noise.

Noise-induced transition from superfluid to vortex state in two-dimensional nonequilibrium polariton condensates: Semianalytical treatment

Noise-induced transition from superfluid to vortex state in two-dimensional nonequilibrium polariton condensates: Semianalytical treatment

Can the Clocks Tick Together Despite the Noise? Stochastic Simulations and Analysis

The suprachiasmatic nucleus (SCN), also known as the circadian master clock, consists of a large population of oscillator neurons. Together, these neurons produce a coherent signal that drives the body’s circadian rhythms. What properties of the cell-to-cell communication allow the synchronization of these neurons, despite a wide range of environmental challenges such as fluctuations in photoperiods? To answer that question, we present a mean-field description of globally coupled neurons modeled as Goodwin oscillators with standard Gaussian noise. Provided that the initial conditions of all neurons are independent and identically distributed, any finite number of neurons becomes independent and has the same probability distribution in the mean-field limit, a phenomenon called propagation of chaos. This probability distribution is a solution to a Vlasov–Fokker–Planck type equation, which can be obtained from the stochastic particle model. We study, using the macroscopic description, how the interaction between external noise and intercellular coupling affects the dynamics of the collective rhythm, and we provide a numerical description of the bifurcations resulting from the noise-induced transitions. Our numerical simulations show a noise-induced rhythm generation at low noise intensities, while the SCN clock is arrhythmic in the high noise setting. Notably, coupling induces resonance-like behavior at low noise intensities, and varying coupling strength can cause period locking and variance dissipation even in the presence of noise.

Unveiling pseudo-crucial events in noise-induced phase transitions

Noise-induced phase transitions are common in various complex systems, from physics to biology. In this article, we investigate the emergence of crucial events in noise-induced phase transition processes and their potential significance for understanding complexity in such systems. We utilize the first-passage time technique and coordinate transformations to study the dynamics of the system and identify crucial events. Furthermore, we employ Diffusion Entropy Analysis, a powerful statistical tool, to characterize the complexity of the system and quantify the information content of the identified events. Our results show that the emergence of crucial events is closely related to the complexity of the system and can provide insight into its behavior. This approach may have applications in diverse fields, such as climate modeling, financial markets, and biological systems, where understanding the emergence of crucial events is of great importance.