Pages similar to: Initial dynamical systems exploration
- Spruce budworm outbreak model
A graphical analysis of a differential equation model reveals how the spruce budworm could devastate forests every 40 years. - A simple spiking neuron model
An introduction to the Fitzhugh Nagumo model of a spiking neuron, including basic phase plane analysis. - Equilibria in discrete dynamical systems
An introduction to the concept of equilibria in discrete dynamical systems and how to calculate them. - The idea of stability of equilibria for discrete dynamical systems
An introduction to the concept of stable and unstable equilibria and how to use cobwebbing to identify stability. - Discrete dynamical systems as function iteration
The simplest versions of discrete dynamical systems can be viewed as evolving due to iterating a function repeatedly. - Solving linear discrete dynamical systems
One can solve a linear discrete dynamical system analytically. The result is an exponential function of the time step. - More details on solving linear discrete dynamical systems
- A graphical approach to finding equilibria of discrete dynamical systems
By plotting the updating function and the diagonal, one can read off the equilibria from their intersections of the two graphs. - The idea of a dynamical system
The basic concept of a dynamical system as the evolution of something over time. The fundamental ideas of the state space and temporal evolution rules are illustrated with examples featuring interactive graphics. - An introduction to discrete dynamical systems
Overview of discrete dynamical systems, focusing on the simplest one-dimensional case, where the dynamics are given by iterating a function. - Developing an initial model to describe bacteria growth
By analyzing some data and hypothesizing rules for cell division, we develop a discrete dynamical system for the growth of a population of bacteria. - Bacteria growth model exercises
Exercises on developing discrete dynamical systems for the growth of a population of bacteria. - Bacteria growth model exercise answers
Answers to selected exercises on developing discrete dynamical systems for the growth of a population of bacteria. - Exponential growth and decay modeled by discrete dynamical systems
Overview of exponential growth and decay in discrete time. Exploration of their qualitative properties as well as solutions to the dynamical system. - Discrete exponential growth and decay exercises
Exercises on solving problems involving exponential growth and decay in discrete time. - Discrete exponential growth and decay exercise answers
Answers to selected exercises on solving problems involving exponential growth and decay in discrete time. - Doubling time and half-life of exponential growth and decay
How exponential growth is characterized by a doubling time and exponential decay is characterized by a half-life. - Constructing a mathematical model for penicillin clearance
We give a word model for how penicillin should be cleared from the blood and allow you to construct a mathematical model to fit some data. - Penicillin clearance model exercises
Exercises and developing discrete dynamical system models for the clearance of penicillin from the blood. - Penicillin clearance model exercise answers
Answers to selected exercises on developing discrete dynamical systems for the clearance of penicillin.