MATH
difference eqns

# Phil hasnip mathematical modelling introduction

• Notes
• 19

This preview shows pages 16–19. Sign up to view the full content.

Phil Hasnip Mathematical Modelling

This preview has intentionally blurred sections. Sign up to view the full version.

Introduction Discrete systems Population analysis Savings account | r | < 1 stable equilibrium different a 0 converge to a | r | > 1 unstable equilibrium different a 0 diverge only get equilibrium if a 0 = a Phil Hasnip Mathematical Modelling
Introduction Discrete systems Population analysis Non-linear case The logistic equation and Verhulst equations are non-linear, e.g.: a n + 1 = r ( 1 - a n ) a n Their behaviour is interesting: 0 < r < 3 stable equilibrium r = 3 oscillation between 2 different values r = 3 . 6 oscillation between 4 different values – period doubling r = 3 . 7 chaos! No pattern or long-term prediction possible Phil Hasnip Mathematical Modelling

This preview has intentionally blurred sections. Sign up to view the full version.

Introduction Discrete systems Population analysis Summary We can use difference equations to model discrete processes approximate continuous processes Long-time behaviour is often of interest Does the model decay or grow? Does the model tend to a limit? Does the model oscillate? Non-linearity -→ chaos! Phil Hasnip Mathematical Modelling
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern