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- Timothy D Sauer
- Physical review. E, Statistical, nonlinear, and…
- 2002

Simulations play a crucial role in the modern study of physical systems. A major open question for long dynamical simulations of physical processes is the role of discretization and truncation errors in the outcome. A general mechanism is described that can cause extremely small noise inputs to result in errors in simulation statistics that are several… (More)

- Timothy D. Sauer
- Scholarpedia
- 2006

- Timothy D Sauer
- Physical review letters
- 2004

We study a general physical network consisting of a collection of response systems with complex nonlinear dynamics, influenced by a common driver. The goal is to reconstruct dynamics, regular or chaotic, that are common to all of the response systems, working from simultaneous time series measured at the responses systems only. A fundamental theorem is… (More)

- Timothy D Sauer, Steven J Schiff
- Physical review. E, Statistical, nonlinear, and…
- 2009

Data assimilation in dynamical networks is intrinsically challenging. A method is introduced for the tracking of heterogeneous networks of oscillators or excitable cells in a nonstationary environment, using a homogeneous model network to expedite the accurate reconstruction of parameters and unobserved variables. An implementation using ensemble Kalman… (More)

- Timothy D. Sauer
- Visual Information Processing
- 1992

Observability and controllability are vitally important in networks, but almost all of the present theory was developed for linear networks without symmetries. To advance beyond the study of such generic networks, we quantify observability and controllability in small (3 node) nonlinear neuronal networks as a function of 1) the connection topology and… (More)

- Andrew J. Whalen, Sean N. Brennan, Timothy D. Sauer, Steven J. Schiff
- 2012 46th Annual Conference on Information…
- 2012

We quantify observability in small (3 node) neuronal networks as a function of 1) the connection topology and symmetry, 2) the measured nodes, and 3) the nodal dynamics (linear and nonlinear). We find that typical observability metrics for 3 neuron motifs range over several orders of magnitude, depending upon topology, and for motifs containing symmetry the… (More)

- Timothy Sauer
- 2013

Stochastic differential equations (SDEs) provide accessible mathematical models that combine deterministic and probabilistic components of dynamic behavior. This article is an overview of numerical solution methods for SDEs. The solutions are stochastic processes that represent diffusive dynamics, a common modeling assumption in many application areas. We… (More)

- Timothy Sauer
- Chaos
- 2003

A general methodology is described for constructing systems that have a slowly converging Lyapunov exponent near zero, based on one-dimensional maps with chaotic attractors. In certain parameter ranges, these relatively simple systems display the properties of intermittent dynamics known as chaotic itinerancy. We show that in addition to the local… (More)

Consider a difference equation whose evolution rule is defined as the maximum of several first-order equations. It is shown that if the first-order equations are individually contractive, then the aggregated max-type equation converges to a fixed point. A corresponding result holds for local convergence.