Student researches chaotic dynamics

Humans have made amazing advances through science, like mapping the human genome, cloning mammals and splitting the atom. But science still can't predict if it'll rain next Tuesday. This is due in part to chaotic dynamics.

Much understanding of the natural world is related to our ability to predict events. Scientists and mathematicians use their understanding to find mathematical relationships in nature. Once they've done this, they can use the math to make predictions about how natural systems will behave. "But if a system's chaotic," noted Colin Kremer, a junior math and biology major, "pretty soon your predictions won't work any more. That's one of the reasons we can't predict the weather more accurately than a few days in advance."

This is also one of the reasons the research that Kremer and Gregg Hartvigsen, associate professor of biology, are working on is so interesting. Weather is probably the most well-known example of chaotic dynamics in nature, but other examples are abound.

Kremer tends to explain his work by way of metaphor. Imagine, he suggested, a field of sunflowers. On each sunflower is a population of insects. The insect group on one individual sunflower is what we call a subpopulation. Each of these subpopulations grows and changes over time as the insects reproduce, die or migrate to other sunflowers. Together, the subpopulations make up a metapopulation.

According to several equations which can predict population dynamics, certain conditions make subpopulations change chaotically, or nonlinearly. This means that two populations which start with slightly different conditions will end up with very different results.

Even though equations indicate that chaotic population growth occurs in nature, scientists don't find it often. Kremer's research may provide an explanation for why. "Maybe we're just missing chaos because we're not looking at the right scale, or it's possible that the kinds of interactions that occur in a real life system moderate the population dynamics, so we're not seeing chaos."

By using his simulation model to link subpopulations together in specific ways, Kremer is hoping to imitate nature and see if the chaotic dynamics could be obscured by the metapopulation structure.

Kremer has continued his research throughout the school year and even though it's been long and sometimes difficult, he's happy to have had the experience. "It's not necessarily a project I'd have stumbled across on my own. But once you take off the first couple of layers and you start to delve deeper into it, it starts to become more interesting as you go along."

Kremer recently gave a poster presentation of his research at the January 2007 Joint Mathematical Meeting of the American Mathematical Society and the Mathematical Association of America where he received an award for his work. Kremer also plans to present his research at the first annual G.R.E.A.T. day at Geneseo on April 17.