Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
- J. Guckenheimer, P. Holmes
- MathematicsApplied Mathematical Sciences
- 1 August 1983
Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples.- Local Bifurcations.- Averaging and Perturbation from a Geometric Viewpoint.-…
The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
- G. Berkooz, P. Holmes, J. Lumley
- Physics
- 1993
It has often been remarked that turbulence is a subject of great scientific and technological importance, and yet one of the least understood (e.g. McComb 1990). To an outsider this may seem strange,…
The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced-choice tasks.
- R. Bogacz, E. Brown, J. Moehlis, P. Holmes, J. Cohen
- Computer SciencePsychology Review
- 1 October 2006
It is proved that there is always an optimal trade-off between speed and accuracy that maximizes various reward functions, including reward rate (percentage of correct responses per unit time), as well as several other objectives, including ones weighted for accuracy.
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
- P. Holmes, J. Lumley, G. Berkooz
- Physics
- 1996
Preface Part I. Turbulence: 1. Introduction 2. Coherent structures 3. Proper orthogonal decomposition 4. Galerkin projection Part II. Dynamical Systems: 5. Qualitative theory 6. Symmetry 7.…
The dynamics of coherent structures in the wall region of a turbulent boundary layer
We have modelled the wall region of a turbulent boundary layer by expanding the instantaneous field in so-called empirical eigenfunctions, as permitted by the proper orthogonal decomposition theorem…
On the Phase Reduction and Response Dynamics of Neural Oscillator Populations
- Eric Shea-Brown, J. Moehlis, P. Holmes
- Computer ScienceNeural Computation
- 1 April 2004
A probabilistic analysis of the response of repetitively firing neural populations to simple pulselike stimuli, exploring the interplay among stimulus duration, baseline firing frequency, and population-level response patterns.
The Dynamics of Legged Locomotion: Models, Analyses, and Challenges
- P. Holmes, R. Full, D. Koditschek, J. Guckenheimer
- BiologySIAM Review
- 1 February 2006
This review describes mathematical models for legged animal locomotion, focusing on rapidly running insects and highlighting past achievements and challenges that remain.
Reward rate optimization in two-alternative decision making: empirical tests of theoretical predictions.
- P. Simen, D. Contreras, Cara L. Buck, Peter T Hu, P. Holmes, J. Cohen
- PsychologyJournal of Experimental Psychology: Human…
- 1 December 2009
The resulting quantitative predictions regarding response time, accuracy, and response bias under these task manipulations were tested and found that grouped data conformed well to the predictions of an optimally parameterized DDM.
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