[5][6] Intraneural communication is affected by dynamic interactions between extracellular fluid pathways.
[7] Information theory draws on thermodynamics in the development of infodynamics that can involve nonlinear systems, especially with regards to the brain.
These mathematical models proved useful and are still used by the field of biophysics today, but a late 20th century development propelled the dynamical study of neurons even further: computer technology.
Computers opened a lot of doors for all of the hard sciences in terms of their ability to approximate solutions to nonlinear equations.
In 2007, a canonical text book was written by Eugene Izhikivech called Dynamical Systems in Neuroscience, assisting the transformation of an obscure research topic into a line of academic study.
(intro needed here) The motivation for a dynamical approach to neuroscience stems from an interest in the physical complexity of neuron behavior.
Different types of neuron models utilize different channels, depending on the physiology of the organism involved.
[12] One of the predominant themes in classical neurobiology is the concept of a digital component to neurons.
This concept was quickly absorbed by computer scientists where it evolved into the simple weighting function for coupled artificial neural networks.
The dynamical criticism of this digital concept is that neurons don't truly exhibit all-or-none firing and should instead be thought of as resonators.
If we give it a big enough push, it will pop out of the lake and roll down the side of the mountain, gaining momentum and going faster.
Let's say we fashioned a loop-de-loop around the base of the mountain so that the ball will shoot up it and return to the lake (no rolling friction or air resistance).
In this example, gravity is the driving force and spatial dimensions x (horizontal) and y (vertical) are the variables.
This property of excitability is what gives neurons the ability to transmit information to each other, so it is important to dynamical neuron networks, but the Morris Lecar can also operate in another parameter regime where it exhibits oscillatory behavior, forever oscillating around in phase space.
Biological neural networks can be modeled by choosing an appropriate biological neuron model to describe the physiology of the organism and appropriate coupling terms to describe the physical interactions between neurons (forming the network).
In terms of nonlinear dynamics, this requires evolving the state of the system through the functions.
, indicating that it is the ith neuron in the network and a coupling function has been added to the first equation.
But the environment is not a simple background, and there is a lot happening right outside of the neuron membrane, in the extracellular space.
[15] Glia, once considered a mere support system for neurons, have been found to serve a significant role in the brain.
Each cell is a tiny community of molecular machinery (organelles) working in tandem and encased in a lipid membrane.
These organelles communicate largely via chemicals like G-proteins and neurotransmitters, consuming ATP for energy.
While neural networks are often associated with artificial intelligence, they have also been productive in the cognitive sciences.
The Lyapunov function is a nonlinear technique used to analyze the stability of the zero solutions of a system of differential equations.
Hopfield networks were specifically designed such that their underlying dynamics could be described by the Lyapunov function.