Journal: Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

Article Title: Structure learning in coupled dynamical systems and dynamic causal modelling

doi: 10.1098/rsta.2019.0048

Figure Lengend Snippet: Glossary of terms that are used in the paper and their description.

Article Snippet: data assimilation [ 12 ] and model identification [ 13 ] , data assimilation is a term that was coined by meteorologists in the mid-twentieth century. It uses (and combines) a wide range of mathematical methods such as non-parametric statistical models (auto regressive models), nonlinear Kalman filters, statistical interpolation, nonlinear time series analysis and nonlinear system identification to establish models useful for weather prediction [ 14 ]. Model identification is a more general term that accounts for constructing models describing a phenomenon, which includes model construction and parameter estimation..

Techniques: Construct, Derivative Assay, Comparison, Selection, Activity Assay, Transformation Assay, Plasmid Preparation, Functional Assay, Diffusion-based Assay, Imaging, Membrane, Magnetic Resonance Imaging, Activation Assay, Generated, Software

Journal: PLoS ONE

Article Title: Analysing Dynamical Behavior of Cellular Networks via Stochastic Bifurcations

doi: 10.1371/journal.pone.0019696

Figure Lengend Snippet: and indicate the areas in which the stochastic trajectories spend most of the time.

Article Snippet: The phenomenon, also known as autonomous stochastic resonance, shows that an optimal amount of noise enhances an intrinsic periodic behavior in stochastic nonlinear systems .

Techniques:

Journal: PLoS ONE

Article Title: Analysing Dynamical Behavior of Cellular Networks via Stochastic Bifurcations

doi: 10.1371/journal.pone.0019696

Figure Lengend Snippet: (A) Probability distributions for and different values of (indicated in the figure). (B) The comparison of probability distributions for the Gillespie algorithm (red curves) and Langevin equations (black curves) calculated for and . (C) Stochastic bifurcation diagram in the − plane. The regions of the diagram are numerated according to the number of maxima of the probability distribution. Lines and stand for the stochastic bifurcations. The dashed vertical lines correspond to a tangent bifurcation (the left line) and the subcritical Hopf bifurcation (the right line) in the deterministic system.

Article Snippet: The phenomenon, also known as autonomous stochastic resonance, shows that an optimal amount of noise enhances an intrinsic periodic behavior in stochastic nonlinear systems .

Techniques: Comparison