arXiv subjects

Ira B. Schwartz

Publications and source records attributed to Ira B. Schwartz.

At least 19 recordsLinked to original sources

arXiv2026

Redirecting counter-moving swarms through collision

Multi-swarm systems, where two or more swarms of mobile agents occupy the same region of space with different parameters and goals, occur in a variety of biological, engineering, and defense applications. Composites of multiple swarms can produce hybrid spatiotemporal patterns, which compared to single swarming systems, are relatively unexplored. In this work, we develop a framework for studying the collision of counter-moving swarms, each with its own preferred, stable velocity before collision. We show that redirection of such swarms after collision occurs when a stable velocity synchronized state of the multi-swarm composite exists. Using a rigid-body approximation, we are able to extract how scatter-redirection transitions scale with swarm parameters in a variety of scenarios from reciprocal and non-reciprocal systems to symmetric and antagonistic parameter values. Our results compare well to simulations of both particle modeled agents and wheeled robots.

nlin.AO↗

arXiv2025

Target-density formation in swarms with stochastic sensing and dynamics

An important goal for swarming research is to create methods for predicting, controlling and designing swarms, which produce collective dynamics that solve a problem through emergent and stable pattern formation, without the need for constant intervention, and with a minimal number of parameters and controls. One such problem involves a swarm collectively producing a desired (target) density through local sensing, motion, and interactions in a domain. Here, we take a statistical physics perspective and develop and analyze a model wherein agents move in a stochastic walk over a networked domain, so as to reduce the error between the swarm density and the target, based on local, random, and uncertain measurements of the current density by the swarming agents. Using a combination of mean-field, small-fluctuation, and finite-number analysis, we are able to quantify how close and how fast a swarm comes to producing a target as a function of sensing uncertainty, stochastic collision rates, numbers of agents, and spatial variation of the target.

nlin.AO↗

arXiv2024

Noise-induced peak intensity fluctuations in class B laser systems

Random perturbations and noise can excite instabilities in population systems that result in large fluctuations. An interesting example involves class B lasers, where the dynamics is determined by the number of carriers and photons in a cavity with noise appearing in the electric-field dynamics. When such lasers are brought above threshold, the field intensity grows away from an unstable equilibrium, exhibiting transient relaxation oscillations with fluctuations due to noise. In this work, we focus on the first peak in the intensity during this transient phase in the presence of noise, and calculate its probability distribution using a Wentzel-Kramers-Brillouin (WKB) approximation. In particular, we show how each value of the first peak is determined by a unique fluctuational-momentum, calculate the peak intensity distribution in the limit where the ratio of photon-to-carrier lifetimes is small, and analyze the behavior of small fluctuations with respect to deterministic theory. Our approach is easily extended to the analysis of transient, noise-induced large fluctuations in general population systems exhibiting relaxation dynamics.

physics.optics↗

arXiv2023

Outbreak-size distributions under fluctuating rates

We study the effect of noisy infection (contact) and recovery rates on the distribution of outbreak sizes in the stochastic SIR model. The rates are modeled as Ornstein-Uhlenbeck processes with finite correlation time and variance, which we illustrate using outbreak data from the RSV 2019-2020 season in the US. In the limit of large populations, we find analytical solutions for the outbreak-size distribution in the long-correlated (adiabatic) and short-correlated (white) noise regimes, and demonstrate that the distribution can be highly skewed with significant probabilities for large fluctuations away from mean-field theory. Furthermore, we assess the relative contribution of demographic and reaction-rate noise on the outbreak-size variance, and show that demographic noise becomes irrelevant in the presence of slowly varying reaction-rate noise but persists for large system sizes if the noise is fast. Finally, we show that the crossover to the white-noise regime typically occurs for correlation times that are on the same order as the characteristic recovery time in the model.

q-bio.PE↗

arXiv2023

Large and small fluctuations in oscillator networks from heterogeneous and correlated noise

Oscillatory networks subjected to noise are broadly used to model physical and technological systems. Due to their nonlinear coupling, such networks typically have multiple stable and unstable states that a network might visit due to noise. In this manuscript, we focus on the assessment of fluctuations resulting from heterogeneous and correlated noise inputs on Kuramoto model networks. We evaluate the typical, small fluctuations near synchronized states and connect the network variance to the overlap between stable modes of synchronization and the input noise covariance. Going beyond small to large fluctuations, we introduce the indicator mode approximation, that projects the dynamics onto a single amplitude dimension. Such an approximation allows for estimating rates of fluctuations to saddle instabilities, resulting in phase slips between connected oscillators. Statistics for both regimes are quantified in terms of effective noise amplitudes that are compared and contrasted for several noise models. Bridging the gap between small and large fluctuations, we show that a larger network variance does not necessarily lead to higher rates of large fluctuations.

nlin.PS↗

arXiv2022

Extreme outbreak dynamics in epidemic models

Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with demographic noise, including the Susceptible-Infected-Recovered (SIR) model and its general extensions. In the limit of large populations, we compute the probability distribution for all extensive outbreaks, including those that entail unusually large or small (extreme) proportions of the population infected. Our approach reveals that, unlike other well-known examples of rare events occurring in discrete-state stochastic systems, the statistics of extreme outbreaks emanate from a full continuum of Hamiltonian paths, each satisfying unique boundary conditions with a conserved probability flux.

q-bio.PE↗

arXiv2021

Critical transition for colliding swarms

Swarming patterns that emerge from the interaction of many mobile agents are a subject of great interest in fields ranging from biology to physics and robotics. In some application areas, multiple swarms effectively interact and collide, producing complex spatiotemporal patterns. Recent studies have begun to address swarm-on-swarm dynamics, and in particular the scattering of two large, colliding swarms with nonlinear interactions. To build on early numerical insights, we develop a mean-field approach that can be used to predict the parameters under which colliding swarms are expected to form a milling state. Our analytical method relies on the assumption that, upon collision, two swarms oscillate near a limit-cycle, where each swarm rotates around the other while maintaining an approximately constant and uniform density. Using this approach we are able to predict the critical swarm-on-swarm interaction coupling, below which two colliding swarms merely scatter, for near head-on collisions as a function of control parameters. We show that the critical coupling corresponds to a saddle-node bifurcation of a stable limit cycle in the uniform, constant density approximation. Our results are tested and found to agree with large multi-agent simulations.

nlin.PS↗

arXiv2021

Interacting Swarm Sensing and Stabilization

Swarming behavior, where coherent motion emerges from the interactions of many mobile agents, is ubiquitous in physics and biology. Moreover, there are many efforts to replicate swarming dynamics in mobile robotic systems which take inspiration from natural swarms. In particular, understanding how swarms come apart, change their behavior, and interact with other swarms is a research direction of special interest to the robotics and defense communities. Here we develop a theoretical approach that can be used to predict the parameters under which colliding swarms form a stable milling state. Our analytical methods rely on the assumption that, upon collision, two swarms oscillate near a limit-cycle, where each swarm rotates around the other while maintaining an approximately constant density. Using our methods, we are able to predict the critical swarm-swarm interaction coupling (below which two colliding swarms merely scatter) for nearly aligned collisions as a function of physical swarm parameters. We show that the critical coupling corresponds to a saddle-node bifurcation of a limit-cycle in the constant-density approximation. Finally, we show preliminary results from experiments in which two swarms of micro UAVs collide and form a milling state, which is in general agreement with our theory.

nlin.AO↗

arXiv2021

Optimal periodic closure for minimizing risk in emerging disease outbreaks

Without vaccines and treatments, societies must rely on non-pharmaceutical intervention strategies to control the spread of emerging diseases such as COVID-19. Though complete lockdown is epidemiologically effective, because it eliminates infectious contacts, it comes with significant costs. Several recent studies have suggested that a plausible compromise strategy for minimizing epidemic risk is periodic closure, in which populations oscillate between wide-spread social restrictions and relaxation. However, no underlying theory has been proposed to predict and explain optimal closure periods as a function of epidemiological and social parameters. In this work we develop such an analytical theory for SEIR-like model diseases, showing how characteristic closure periods emerge that minimize the total outbreak, and increase predictably with the reproductive number and incubation periods of a disease, as long as both are within predictable limits. Using our approach we demonstrate a sweet-spot effect in which optimal periodic closure is maximally effective for diseases with similar incubation and recovery periods. Our results compare well to numerical simulations, including in COVID-19 models where infectivity and recovery show significant variability.

q-bio.PE↗

arXiv2020

Stability of milling patterns in self-propelled swarms on surfaces

In some physical and biological swarms, agents effectively move and interact along curved surfaces. The associated constraints and symmetries can affect collective-motion patterns, but little is known about pattern stability in the presence of surface curvature. To make progress, we construct a general model for self-propelled swarms moving on surfaces using Lagrangian mechanics. We find that the combination of self-propulsion, friction, mutual attraction, and surface curvature produce milling patterns where each agent in a swarm oscillates on a limit cycle, with different agents splayed along the cycle such that the swarm's center-of-mass remains stationary. In general, such patterns loose stability when mutual attraction is insufficient to overcome the constraint of curvature, and we uncover two broad classes of stationary milling-state bifurcations. In the first, a spatially periodic mode undergoes a Hopf bifurcation as curvature is increased which results in unstable spatiotemporal oscillations. This generic bifurcation is analyzed for the sphere and demonstrated numerically for several surfaces. In the second, a saddle-node-of-periodic-orbits occurs in which stable and unstable milling states collide and annihilate. The latter is analyzed for milling states on cylindrical surfaces. Our results contribute to the general understanding of swarm pattern-formation and stability in the presence of surface curvature, and may aid in designing robotic swarms that can be controlled to move over complex surfaces.

nlin.AO↗

arXiv2020

Unstable oscillations and bistability in delay-coupled swarms

It is known from both theory and experiments that introducing time delays into the communication network of mobile-agent swarms produces coherent rotational patterns. Often such spatio-temporal rotations can be bistable with other swarming patterns, such as milling and flocking. Yet, most known bifurcation results related to delay-coupled swarms rely on inaccurate mean-field techniques. As a consequence, the utility of applying macroscopic theory as a guide for predicting and controlling swarms of mobile robots has been limited. To overcome this limitation, we perform an exact stability analysis of two primary swarming patterns in a general model with time-delayed interactions. By correctly identifying the relevant spatio-temporal modes that determine stability in the presence of time delay, we are able to accurately predict bistability and unstable oscillations in large swarm simulations-- laying the groundwork for comparisons to robotics experiments.

nlin.AO↗

arXiv2019

Network desynchronization by non-Gaussian fluctuations

Many networks must maintain synchrony despite the fact that they operate in noisy environments. Important examples are stochastic inertial oscillators, which are known to exhibit fluctuations with broad tails in many applications, including electric power networks with renewable energy sources. Such non-Gaussian fluctuations can result in rare network desynchronization. Here we build a general theory for inertial oscillator network desynchronization by non-Gaussian noise. We compute the rate of desynchronization and show that higher-moments of noise enter at specific powers of coupling: either speeding up or slowing down the rate exponentially depending on how noise statistics match the statistics of a network's slowest mode. Finally, we use our theory to introduce a technique that drastically reduces the effective description of network desynchronization. Most interestingly, when instability is associated with a single edge, the reduction is to one stochastic oscillator.

nlin.AO↗

arXiv2018

Rare slips in fluctuating synchronized oscillator networks

We study rare phase slips due to noise in synchronized Kuramoto oscillator networks. In the small-noise limit, we demonstrate that slips occur via large fluctuations to saddle phase-locked states. For tree topologies, slips appear between subgraphs that become disconnected at a saddle-node bifurcation, where phase-locked states lose stability generically. This pattern is demonstrated for sparse networks with several examples. Scaling laws are derived and compared for different tree topologies. On the other hand, for dense networks slips occur between oscillators on the edges of the frequency distribution. If the distribution is discrete, the probability-exponent for large fluctuations to occur scales linearly with the system size. However, if the distribution is continuous, the probability is a constant in the large network limit, as individual oscillators fluctuate to saddles while all others remain fixed. In the latter case, the network's coherence is approximately preserved.

cond-mat.dis-nn↗

arXiv2018

The Dynamics of Interacting Swarms

Swarms are self-organized dynamical coupled agents which evolve from simple rules of communication. They are ubiquitous in nature, and be- coming more prominent in defense applications. Here we report on a preliminary study of swarm collisions for a swarm model in which each agent is self-propelling but globally communicates with other agents. We generalize previous models by investigating the interacting dynamics when delay is introduced to the communicating agents. One of our major find- ings is that interacting swarms are far less likely to flock cohesively if they are coupled with delay. In addition, parameter ranges based on coupling strength, incidence angle of collision, and delay change dramatically for other swarm interactions which result in flocking, milling, and scattering.

nlin.AO↗

arXiv2018

Enhancement of large fluctuations to extinction in adaptive networks

During an epidemic, individual nodes in a network may adapt their connections to reduce the chance of infection. A common form of adaption is avoidance rewiring, where a noninfected node breaks a connection to an infected neighbor and forms a new connection to another noninfected node. Here we explore the effects of such adaptivity on stochastic fluctuations in the susceptible-infected-susceptible model, focusing on the largest fluctuations that result in extinction of infection. Using techniques from large-deviation theory, combined with a measurement of heterogeneity in the susceptible degree distribution at the endemic state, we are able to predict and analyze large fluctuations and extinction in adaptive networks. We find that in the limit of small rewiring there is a sharp exponential reduction in mean extinction times compared to the case of zero adaption. Furthermore, we find an exponential enhancement in the probability of large fluctuations with increased rewiring rate, even when holding the average number of infected nodes constant.

nlin.AO↗

arXiv2017

Model Reduction in Stochastic Environments

We present a general theory of stochastic model reduction which is based on a normal form coordinate transform method of A.J. Roberts. This nonlinear, stochastic projection allows for the deterministic and stochastic dynamics to interact correctly on the lower-dimensional manifold so that the dynamics predicted by the reduced, stochastic system agrees well with the dynamics predicted by the original, high-dimensional stochastic system. The method may be applied to any system with well-separated time scales. In this article, we consider a physical problem that involves a singularly perturbed Duffing oscillator as well as a biological problem that involves the prediction of infectious disease outbreaks.

math.DS↗

arXiv2017

Asymmetric noise-induced large fluctuations in coupled systems

Networks of interacting, communicating subsystems are common in many fields, from ecology, biology, epidemiology to engineering and robotics. In the presence of noise and uncertainty, inter- actions between the individual components can lead to unexpected complex system-wide behaviors. In this paper, we consider a generic model of two weakly coupled dynamical systems, and show how noise in one part of the system is transmitted through the coupling interface. Working synergistically with the coupling, the noise on one system drives a large fluctuation in the other, even when there is no noise in the second system. Moreover, the large fluctuation happens while the first system exhibits only small random oscillations. Uncertainty effects are quantified by showing how characteristic time scales of noise induced switching scale as a function of the coupling between the two coupled parts of the experiment. In addition, our results show that the probability of switching in the noise-free system scales inversely as the square of reduced noise intensity amplitude, rendering the virtual probability of switching to be an extremely rare event. Our results showing the interplay between transmitted noise and coupling are also confirmed through simulations, which agree quite well with analytic theory.

cond-mat.stat-mech↗

arXiv2017

Large order fluctuations, switching, and control in complex networks

We propose an analytical technique to study large fluctuations and switching from internal noise in complex networks. Using order-disorder kinetics as a generic example, we construct and analyze the most probable, or optimal path of fluctuations from one ordered state to another in real and synthetic networks. The method allows us to compute the distribution of large fluctuations and the time scale associated with switching between ordered states for networks consistent with mean-field assumptions. In general, we quantify how network heterogeneity influences the scaling patterns and probabilities of fluctuations. For instance, we find that the probability of a large fluctuation near an order-disorder transition decreases exponentially with the participation ratio of a network's principle eigenvector -- measuring how many nodes effectively contribute to an ordered state. Finally, the proposed theory is used to answer how and where a network should be targeted in order to optimize the time needed to observe a switch.

physics.soc-ph↗