I have a new project at school for my Numerical Computing course, and I’m very excited:

Project 3: Modeling with Ordinary Differential Equations
Due Tuesday, April 14, 2009

  • Create a mathematical model of some real world system using ODEs (e.g. population models, physics models).
  • Numerically solve these ODEs for a variety of initial conditions, so many possible behaviors can be studied.

For this project, I am planning on creating a model that follows the systems describing three distinct populations, each located in post-apocalyptic North America.

In this theoretical model, I will have a human population, a robotic population, and a nanorobotic population. They will each compete against the others in a free-for-all.

Humans

  • They may start with a population well above 300 million.
  • They will experience normal population growth, but the growth may be influenced by a carrying capacity and, to a minor extent, available sunlight (for solar cells).
  • They will experience a technological breakthrough each subsequent year, increasing exponentially; this will help them wage war with the other populations.

Robots

  • They may start with a population in the tens of millions, possibly thousands.
  • Each quarter year, they will experience both a technological breakthrough and an increase in population, the breakthroughs increasing exponentially each quarter; this will help them wage war with the other populations as well as increase their rate of growth.
  • The growth rate will be directly influenced by the amount of available sunlight.

Nanorobots

  • They will experience an extremely high growth rate, similar to bacteria; this rate is sunlight and competing population biomass dependent, meaning that they will be powered through solar cells and through the consumption of the competing populations.
  • The efficiency of their ability to kill / convert competing populations into biomass is directly related to sunlight.
  • A swarm of nanobots will eventually blot out the light given from the sun, affecting the sunlight for a large majority of nanobots as well as both competing species.

None of these populations have the immediate ability to travel into space, so growth factors are dependent on the amount of power available for solar cells. The nanorobots have potentially unlimited population potential, capped by the raw biomass they consume and the maximum sunlight available.