Simulating, analyzing, and animating dynamical systems - a guide to XPPAUT for researchers and students

By B. Ermentrout. Software, environments, tools, 2002

1,984 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e02f0051f2b514c0ee5c9191d0714db6c6495ce4

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In Numerical Analysis

Citations in the corpus

BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models (2010, methodology): “To permit a given model to be simulated conveniently, BioModels Database also provides downloadable configuration files for open tools such as XPPAUT [57,58] and SciLab [30].”
The Dynamics of Legged Locomotion: Models, Analyses, and Challenges (2006, methodology): “or calculated by use of adjoint theory [182], as implemented, for example, in the software XPP [115].”
Geometric singular perturbation analysis of an autocatalator model (2009, methodology): “We illustrate these results with numerical simulations obtained by using the software XPPAUT [ 6 ].”
High Frequency Stimulation of the Subthalamic Nucleus Eliminates Pathological Thalamic Rhythmicity in a Computational Model (2004, methodology): “Simulations were performed on personal computers using the software XPP (Ermentrout, 2002).”
On the Phase Reduction and Response Dynamics of Neural Oscillator Populations (2004, methodology): “Figure 4 compares these formulas with PRCs calculated using XPP (Ermentrout, 2002) for the HR, FN, HH, and ML models near the relevant bifurcations (PRCs for the integrate-and-re models are exact).”
Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (2006, background): “1) – the result is known as the Pontryagin–Rodygin (1960) theorem.”
Stability of a class of linear switching systems with time delay (2006, methodology): “The numerical simulations were done with XPPAUT [ 27 ] which is a software package that performs numerical integration of delay dieren tial equations.”
Global analysis of a Holling type II predator–prey model with a constant prey refuge (2014, methodology): “To confirm those points, we employed the bifurcation software XPPaut [12] to carry out one-parameter (here the prey refuge parameter c) bifurcation analysis with all other parameter values fixed as those in Fig.”
Active Brownian particles (2012, methodology): “The comparison of the stationary solutions of the reduced systems with the corresponding solutions of the full systems obtained with XPPAUT/AUTO reveals a differences at low velocity alignment strengths µ (Fig.”
Simulation of networks of spiking neurons: A review of tools and strategies (2006, neutral): “A book has been written on the use of the program (Ermentrout 2004); and it comes with 120 pages of documentation and dozens of examples.”