MAT 1330 Lecture Notes - Lecture 31: Caffeine

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1330
• Professor: Rachelle Miron

Document Summary

3 discrete-time dynamical systems (dtds) - part i. Goal: find a mathematical description for dynamic processes in nature. Idea: project forward from one generation to the next. A function describes how the initial measurement and the nal measurement in an experiment are related. De nition: a dtds is an assignment of the form xt+1 = f(xt), where xt is the state of the system at time t and f is the updating function. Examples: constant addition between generations (e. g. trees): xt+1 = xt + c, constant multiple between generations (e. g. bacteria): xt+1 = rxt, constant decay and addition (e. g. medication): xt+1 = rxt + c with 0 < r < 1. De nition: a solution of a dtds is a sequence of numbers that describes the future of the system, i. e. {x0, x1, x2, . with the property that xt+1 = f(xt). Note: a solution is not a single number but an entire in nite sequence.