scholarly journals Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics

2020 ◽  
Vol 25 (4) ◽  
pp. 62
Author(s):  
Paweł Olejnik
Keyword(s):  
Nonlinear Dynamics ◽  
Computational Methods ◽  
Applied Mathematics

Nonlinear dynamics takes its origins from physics and applied mathematics [...]

scholarly journals Reduced Dimension, Biophysical Neuron Models Constructed From Observed Data

2021 ◽  
Author(s):  
Randall Clark ◽  
Lawson Fuller ◽  
Jason Platt ◽  
Henry D. I. Abarbanel
Keyword(s):  
Nonlinear Dynamics ◽  
Biological Networks ◽  
Applied Mathematics ◽  
Voltage Response ◽  
Synaptic Connections ◽  
Neuron Models ◽  
Detailed Specification ◽  
Reduced Dimension ◽  
The Many ◽  
Voltage Dynamics

AbstractUsing methods from nonlinear dynamics and interpolation techniques from applied mathematics, we show how to use data alone to construct discrete time dynamical rules that forecast observed neuron properties. These data may come from from simulations of a Hodgkin-Huxley (HH) neuron model or from laboratory current clamp experiments. In each case the reduced dimension data driven forecasting (DDF) models are shown to predict accurately for times after the training period.When the available observations for neuron preparations are, for example, membrane voltage V(t) only, we use the technique of time delay embedding from nonlinear dynamics to generate an appropriate space in which the full dynamics can be realized.The DDF constructions are reduced dimension models relative to HH models as they are built on and forecast only observables such as V(t). They do not require detailed specification of ion channels, their gating variables, and the many parameters that accompany an HH model for laboratory measurements, yet all of this important information is encoded in the DDF model.As the DDF models use only voltage data and forecast only voltage data they can be used in building networks with biophysical connections. Both gap junction connections and ligand gated synaptic connections among neurons involve presynaptic voltages and induce postsynaptic voltage response. Biophysically based DDF neuron models can replace other reduced dimension neuron models, say of the integrate-and-fire type, in developing and analyzing large networks of neurons.When one does have detailed HH model neurons for network components, a reduced dimension DDF realization of the HH voltage dynamics may be used in network computations to achieve computational efficiency and the exploration of larger biological networks.

One Hundred Years of the Galerkin Method

2017 ◽  
Vol 17 (3) ◽  
pp. 351-357 ◽  
Author(s):  
Sergey Repin
Keyword(s):  
Galerkin Method ◽  
Computational Methods ◽  
Applied Mathematics ◽  
Special Volume ◽  
Hundredth Anniversary ◽  
Biennial Conference ◽  
Introductory Article ◽  
Remarkable Event ◽  
The Galerkin Method ◽  
The University

AbstractIn 2016, the biennial conference Computational Methods in Applied Mathematics (CMAM) was dedicated to a remarkable event: the hundredth anniversary of the Galerkin method. This special volume of the same name journal is mainly based on the papers of participants of this conference. The introductory article contains a brief description of the origin and development of the Galerkin method and gives an overview of the conference, which was held at the University of Jyväskylä (Finland), July 31 – August 6, 2016.

Sign in / Sign up

Export Citation Format

Share Document