LIFESCI 30B Lecture Notes - Lecture 1: Attractor
Document Summary
Almost any collection of interacting objects can be viewed as a dynamical system: Animal populations (ecology) (various subsystems of) living organisms (biology) The basic purpose of a mathematical model is to allow us to predict the long-term behavior of the system. In particular we want to be able to predict how the system will respond to interventions. Both oscillations are regular, with a period of about 10 years. The oscillations are synchronized, with a time delay. Our simple model of systems like the lynx-hare system was called the shark tuna model: In the st model, only four things could happen: Sharks are born, shark die (one way or another) Tuna are born, tuna die by getting eaten by sharks. Nevertheless, this model predicts the synchronized oscillations observed in systems like the lynx-hare system. It "remembers" the effect of an intervention forever.
