Math Insight

Pages similar to: Spruce budworm outbreak model

• 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.
• A simple spiking neuron model
  An introduction to the Fitzhugh Nagumo model of a spiking neuron, including basic phase plane analysis.
• 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.
• 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.
• Initial dynamical systems exploration
  Exploring models of anteater population growth and lead decay in the bloodstream using interactive applets.
• 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.
• Introduction to visualizing differential equation solutions in the phase plane
  
• 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
  

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