1 / 4

Understanding Linear Systems: Equilibrium Solutions & Competing Stores Model

Explore properties of linear systems and the linearity principle, with examples like harmonic oscillators and the competing stores model. Experiment with equilibrium solutions and values to analyze their effects. Quantities and explanations included. Dive deeper into the topic with readings and exercises provided.

syshe
Télécharger la présentation

Understanding Linear Systems: Equilibrium Solutions & Competing Stores Model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Section 3.1 PROPERTIES OF LINEAR SYSTEMS AND THE LINEARITY PRINCIPLE

  2. Intro to linear systems Lots of useful systems of DEs are in the form Examples include the damped (or undamped) harmonic oscillator (see p. 234) and the competing stores model (see p. 235). Use LinearPhasePortraits to experiment with different values of a, b, c, and d.

  3. Equilibrium solutions Find the equilibrium solution(s) to Do the values of a, b, c, and d have an effect on the equilibrium solution(s)?

  4. Competing stores model Read p. 235-237. Quantities: • x(t) = daily profit of Paul’s store at time t. • y(t) = daily profit of Bob’s store at time t. • a = effect of Paul’s profits on the change in Paul’s profits. Explain: a > 0 means ___; a < 0 means ___. • b = effect of Bob’s profits on the change in Paul’s profits. Explain: b > 0 means ___; b < 0 means ___. • Explain c and d. Do p. 252 1-4.

More Related