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- Luis Mier-y-Teran-Romero, Eric Forgoston, Ira B. Schwartz
- 2011 IEEE/RSJ International Conference on…
- 2011

We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a translating state and a rotating state with stationary center of mass. Time delayed communication creates a bifurcation… (More)

- Eric Forgoston, Ira B Schwartz
- Physical review. E, Statistical, nonlinear, and…
- 2008

We consider a general model of self-propelling particles interacting through a pairwise attractive force in the presence of noise and communication time delay. Previous work by Erdmann [Phys. Rev. E 71, 051904 (2005)] has shown that a large enough noise intensity will cause a translating swarm of individuals to transition to a rotating swarm with a… (More)

- Ira B Schwartz, Eric Forgoston, Simone Bianco, Leah B Shaw
- Journal of the Royal Society, Interface
- 2011

Extinction appears ubiquitously in many fields, including chemical reactions, population biology, evolution and epidemiology. Even though extinction as a random process is a rare event, its occurrence is observed in large finite populations. Extinction occurs when fluctuations owing to random transitions act as an effective force that drives one or more… (More)

- Eric Forgoston, Lora Billings, Ira B Schwartz
- Chaos
- 2009

We consider a stochastic susceptible-exposed-infected-recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the associated, reduced set of stochastic evolution equations. The transformation correctly projects both the dynamics and the noise… (More)

- M. Ani Hsieh, Eric Forgoston, T. William Mather, Ira B. Schwartz
- 2012 IEEE International Conference on Robotics…
- 2012

Tracking Lagrangian coherent structures in dynamical systems is important for many applications such as oceanography and weather prediction. In this paper, we present a collaborative robotic control strategy designed to track stable and unstable manifolds. The technique does not require global information about the fluid dynamics, and is based on local… (More)

- Eric Forgoston, Lora Billings, Philip Yecko, Ira B Schwartz
- Chaos
- 2011

We consider the problem of stochastic prediction and control in a time-dependent stochastic environment, such as the ocean, where escape from an almost invariant region occurs due to random fluctuations. We determine high-probability control-actuation sets by computing regions of uncertainty, almost invariant sets, and Lagrangian coherent structures. The… (More)

- Matthew Michini, M. Ani Hsieh, Eric Forgoston, Ira B. Schwartz
- IEEE Transactions on Robotics
- 2014

Lagrangian coherent structures (LCSs) are separatrices that delineate dynamically distinct regions in general dynamical systems and can be viewed as the extensions of stable and unstable manifolds to general time-dependent systems. Identifying LCS in dynamical systems is useful for many applications, including oceanography and weather prediction. In this… (More)

- Eric Forgoston, Simone Bianco, Leah B Shaw, Ira B Schwartz
- Bulletin of mathematical biology
- 2011

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying… (More)

Established theory addresses the idea that herbivory can have positive feedbacks on nutrient flow to plants. Positive feedbacks likely emerge from a greater availability of organic carbon that primes the soil by supporting nutrient turnover through consumer and especially microbially-mediated metabolism in the detrital pool. We developed an entirely novel… (More)

- Eric Forgoston, Ira B Schwartz
- Bulletin of mathematical biology
- 2013

We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the lower dimensional manifold on which the deterministic and stochastic dynamics correctly interact. Our method produces a… (More)