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A simple spiking neuron model
Spruce budworm outbreak model
A graphical analysis of a differential equation model reveals how the spruce budworm could devastate forests every 40 years.
The Forward Euler algorithm for solving an autonomous differential equation
Using the linear approximation, or tangent line, to the solution of a differential equation to estimate the solution over small intervals.
Introduction to bifurcations of a differential equation
Representing the influence of a parameter on the behavior of a differential equation in terms of a bifurcation diagram of equilibria.
Initial dynamical systems exploration
Exploring models of anteater population growth and lead decay in the bloodstream using interactive applets.
An introduction to ordinary differential equations
An introduction using simple examples explaining what an ordinary differential equation is and how one might solve them.
Exponential growth and decay: a differential equation
Solving a differential equation to find an unknown exponential function.
Solving single autonomous differential equations using graphical methods
Using graphical methods, one can observe where the rate of change is positive or negative and determine the behavior of a solution to a differential equation.
Single autonomous differential equation problems
Sample problems involving analysis of a single autonomous differential equation.
Two dimensional autonomous differential equation problems
Sample problems involving analysis of a two coupled autonomous differential equations.
Solutions to two dimensional autonomous differential equation problems
Solutions to sample problems involving analysis of a two coupled autonomous differential equations.
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.
Ordinary differential equation examples
Simple examples of solving ordinary differential equation.
Solving linear ordinary differential equations using an integrating factor
Illustration of the procedure to find an integrating factor that allows integration of a first order linear ordinary differential equation.
Examples of solving linear ordinary differential equations using an integrating factor
Examples of finding an integrating factor and integrating first order linear ordinary differential equations.
Another differential equation: projectile motion
Calculating an equation for the position of an object acted upon by only gravity.
A simple spiking neuron model