arXiv subjects

Jason Hindes

Publications and source records attributed to Jason Hindes.

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↗

arXiv2026

Time delay in the 1d swarmalator model

We study the 1d swarmalator model augmented with time delayed coupling. Along with the familiar sync, async, and phase wave states, we find a family of unsteady states where the order parameters are time periodic, sometimes with clean oscillations, sometimes with irregular vacillations. The unsteady states are born in two ways: via a Hopf bifurcation from the phase wave, and a zero eigenvalue bifurcation from the async state. We find both of these boundary curves analytically. A surprising result is that stabilities of the async and sync states are independent of the delay {\tau}; they depend only on the coupling strength.

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↗

arXiv2025

Multi-rank Subspace Change-point Detection with Application in Monitoring Robotic Swarms

We study real-time detection of low-rank changes in the covariance structure of high-dimensional streaming data, motivated by robotic swarm monitoring. Building on the spiked covariance model, we propose the Multi-rank Subspace-CUSUM (MRS-C) procedure, which extends classical CUSUM by tracking projection energy onto an estimated signal subspace. We analyze the immediate-change expected detection delay (EDD), deriving closed-form choices of the window size and drift parameter that minimize the leading-order asymptotic EDD approximation. We further establish an oracle-relative asymptotic efficiency result, with an explicit efficiency constant that depends on heterogeneity in spike strengths. When the signal rank is unknown, we propose a practical parallel procedure. Simulations and robotic swarm-behavior data illustrate robustness and effectiveness.

stat.ME↗

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↗

arXiv2023

The chaotic milling behaviors of interacting swarms after collision

We consider the problem of characterizing the dynamics of interacting swarms after they collide and form a stationary center of mass. Modeling efforts have shown that the collision of near head-on interacting swarms can produce a variety of post-collision dynamics including coherent milling, coherent flocking, and scattering behaviors. In particular, recent analysis of the transient dynamics of two colliding swarms has revealed the existence of a critical transition whereby the collision results in a combined milling state about a stationary center of mass. In the present work we show that the collision dynamics of two swarms that form a milling state transitions from periodic to chaotic motion as a function of the repulsive force strength and its length scale. We used two existing methods as well as one new technique: Karhunen-Loeve decomposition to show the effective modal dimension chaos lives in, the 0-1 test to identify chaos, and then Constrained Correlation Embedding to show how each swarm is embedded in the other when both swarms combine to form a single milling state after collision. We expect our analysis to impact new swarm experiments which examine the interaction of multiple swarms.

nlin.PS↗

arXiv2022

SIS model of disease extinction on heterogeneous directed population networks

Understanding the spread of diseases through complex networks is of great interest where realistic, heterogeneous contact patterns play a crucial role in the spread. Most works have focused on mean-field behavior -- quantifying how contact patterns affect the emergence and stability of (meta)stable endemic states in networks. On the other hand, much less is known about longer time scale dynamics, such as disease extinction, whereby inherent process stochasticity and contact heterogeneity interact to produce large fluctuations that result in the spontaneous clearance of infection. Here we show that heterogeneity in both susceptibility and infectiousness (incoming and outgoing degree, respectively) has a non-trivial effect on extinction in directed contact networks, both speeding-up and slowing-down extinction rates depending on the relative proportion of such edges in a network, and on whether the heterogeneities in the incoming and outgoing degrees are correlated or anticorrelated. In particular, we show that weak anticorrelated heterogeneity can increase the disease stability, whereas strong heterogeneity gives rise to markedly different results for correlated and anticorrelated heterogeneous networks. All analytical results are corroborated through various numerical schemes including network Monte-Carlo simulations.

cond-mat.stat-mech↗

arXiv2022

Finite-time Correlations Boost Large Voltage-Angle Fluctuations in Electric Power Grids

Decarbonization in the energy sector has been accompanied by an increased penetration of new renewable energy sources in electric power systems. Such sources differ from traditional productions in that, first, they induce larger, undispatchable fluctuations in power generation and second, they lack inertia. Therefore, substituting new renewables for traditional generation induces stronger and more frequent disturbances and modifies the way disturbances propagate across AC electric power grids. Recent measurements have indeed reported long, non-Gaussian tails in the distribution of local grid-frequency data. Large frequency deviations may induce grid instabilities, leading in worst-case scenarios to cascading failures and large-scale blackouts. In this manuscript, we investigate how correlated noise disturbances, characterized by the cumulants of their distribution, propagate through meshed, high-voltage power grids. We show that for a single source of fluctuations, non-Gaussianities in the form of finite skewness and positive kurtosis of the noise distribution propagate over the entire network when the noise correlation time is larger than the network's intrinsic time scales, but that they vanish over short distances if the noise fluctuates rapidly. We furthermore show that a Berry-Esseen theorem leads to the vanishing of non-Gaussianities as the number of uncorrelated noise sources increases. Our results show that the persistence of non-Gaussian fluctuations of feed-in power have a global impact on power-grid dynamics when they fluctuate over time scales larger than the intrinsic time scales of the system, which, we argue, is the relevant regime in real power grids. Our predictions are corroborated by numerical simulations on realistic models of power grids.

nlin.AO↗

arXiv2021

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

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

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↗

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

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

Torus bifurcations of large-scale swarms having range dependent communication delay

Dynamical emergent patterns of swarms are now fairly well established in nature, and include flocking and rotational states. Recently, there has been great interest in engineering and physics to create artificial self-propelled agents that communicate over a network and operate with simple rules, with the goal of creating emergent self-organizing swarm patterns. In this paper, we show that when communicating networks have range dependent delays, rotational states which are typically periodic, undergo a bifurcation and create swarm dynamics on a torus. The observed bifurcation yields additional frequencies into the dynamics, which may lead to quasi-periodic behavior of the swarm.

nlin.AO↗

arXiv2020

Delay Induced Swarm Pattern Bifurcations in Mixed Reality Experiments

Swarms of coupled mobile agents subject to inter-agent wireless communication delays are known to exhibit multiple dynamic patterns in space that depend on the strength of the interactions and the magnitude of the communication delays. We experimentally demonstrate communication delay-induced bifurcations in the spatio-temporal patterns of robot swarms using two distinct hardware platforms in a mixed reality framework. Additionally, we make steps toward experimentally validating theoretically predicted parameter regions where transitions between swarm patterns occur. We show that multiple rotation patterns persist even when collision-avoidance strategies are incorporated, and we show the existence of multi-stable, co-existing rotational patterns not predicted by usual mean field dynamics. Our experiments are the first significant steps towards validating existing theory and the existence and robustness of the delay-induced patterns in real robotic swarms.

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↗