Section 22.12

Modeling with Systems

From biology to engineering, coupled rates of change appear everywhere.

1

Introduction

Many systems involve multiple interacting quantities:

  • Two tanks exchanging fluid.
  • Rabbits (prey) and Foxes (predators).
  • Voltage and Current in circuits.
2

Example 1: Mixing

The Setup

Tank A holds 100L. Tank B holds 100L.
Water flows A B at 5L/min.
Water flows B A at 5L/min.
Salt flows with the water.

Equations:


3

Example 2: Lotka-Volterra

Interactive: Rabbits vs Foxes

The linear system near equilibrium is a "Center". The populations oscillate forever (in this simple model).

4

Example 3: RLC Network

Multiple loops in a circuit utilize Kirchhoff's Laws.
Loop 1: .
Loop 2: .

This forms a coupled system of differential equations for currents and charge .

5

Practice Quiz

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