|Date||Nov 07, 2014|
The meaningful distance for biological organisms is not necessarily given by the Euclidean metric, but possibly by a one related to the amount of resources such as food. It is assumed that the migration distance of biological organisms is measured by the amount of food between two points. A new chemotaxis model is introduced as an application of this ``metric of food”. It is shown that, if the length of the random walk is given by such a metric, the well-known traveling wave phenomena of the chemotaxis theory can be obtained without the typical assumption that microscopic scale bacteria may sense the macroscopic scale gradient chemical concentration. The uniqueness and existence of traveling solutions of pulse and front types are proved. This is a joint work with Dr. Sunho Choi.