Winter 2022: Spatiotemporal dynamics

Physics 239: Spatiotemporal Dynamics in Biological Systems 

Instructor: Prof. Terry Hwa; office: Urey 7222
phone: 4-7263; e-mail: 
TA: Dr. Leonardo Pucciani-Mori (Leo)
Time: M W 9:30am – 10:50 am
[also selected Fridays may be used for tutorials and/or make-up lectures]
Location: Jan 3-17: online only per UCSD COVID policy; 
Office Hour: after class or by appointment
Course URL: this page (
Grade 3-4 problem sets and 1-2 group projects
Prerequisite: a solid first course in ordinary differential equation; exposure to partial differential equation; interest in biological phenomena. 

Reference Books

Course description: 

This is a new course aimed at advanced undergraduates and beginning graduate students in physics, engineering, and mathematics. Most of the course should also be accessible to BIO students with a strong background in math through ODE. The course teaches and applies basic concepts in dynamical systems (phase plots, stability analysis, Lyapunov function) and pattern formation in spatially extended systems (Fisher wave, Keller-Segel, Turing instability, excitable systems, etc). The specific topics to be discussed will be taken from concrete biological problems from ecology, evolution, and developmental biology. Lessons learned from the analysis will be gleaned for biological insight.

Course outline

  • Introduction to bacterial growth, population dynamics, and ecology
  • Lotka-Volterra model and its generalization: fixed points and phase diagrams
  • Consumer-Resource model: coexistence and global stability
  • Trophic interactions, cross-feeding, cooperation, and cheating
  • Spatial range expansion: Fisher-Kolmogorov wave and the stability criterion
  • Bacterial chemotaxis: coordination of migration and growth
  • Turing instability and patterns in developmental biology
  • Excitable systems: pulses and spiral waves

Tentative course outline:

  Date Topics assignment
L1 M, Jan 3 Course overview and intro to population dynamics:
logistic growth and the effect of predation
[note] [YouTube recording]
L2 W, Jan 5 Simple models of interaction: predator-prey dynamics
[note] [YouTube recording]
HW1 due Wed
Jan 19
L3 M, Jan 10 Simple models of interaction (cont’d): spread of epidemic
[note] [YouTube recording]
  M, Jan 10 TA tutorial 
[note] [YouTube recording]
L4 W, Jan 12 Generalized Lotka-Volterra model: stability analysis
[note] [YouTube recording]
  M, Jan 17 Martin Luther King Jr Day (no class)  
L5 W, Jan 19 Models of oscillation: predator-prey dynamics revisited
[note] [YouTube recording]
HW2 (modified)
due Wed Feb 2
L6 M, Jan 24 excitable systems and relaxational oscillators
[note] [YouTube recording]
HW1 solution
L7 W, Jan 26 Consumer-resource model: continuous culture
[note] [YouTube recording]
L8 M, Jan 31 bacterial growth physiology 
[note (updated Feb 6)] [YouTube recording]
  M, Jan 31 TA tutorial   
L9 W, Feb 2 Monod growth law and generalization to 2 nutrients
[continuation of L8 note] [YouTube recording]
 HW2 solution
L10 M, Feb 7 CR model of competition: 2-species and 2-nutrients
[note] [YouTube recording]
 HW3 (modified)
 due Wed Feb 23
L11 W, Feb 9 Tilman’s graphic method [note from Feb 7]
MacArthur’s solution to the generalized CR model
[note] [YouTube recording]
L12 M, Feb 14 MacArthur’s ecological exclusion principle
[continuation of L11 note];  
feasibility and phase diagram
[note] [YouTube recording]
L13 W, Feb 16 proteome-constrained CR model
[note] [YouTube recording]
  M, Feb 21 President’s Day (no class)  
L14 W, Feb 23 Consumer-resource model of symbiosis I:
Syntrophic interaction from metabolic exchanges
[note] [YouTube recording]
due Wed Mar 9
L15 F, Feb 25
Consumer-resource model of symbiosis II:
producers, cheaters, and cooperators
[note (updated)] [YouTube recording]
L16 M, Feb 28 Population range expansion: Fisher-Kolmogorov equation and stability; trigger wave
[note] [YouTube recording]
HW4b (more problems included
L17 W, Mar 2 Chemotaxis: Keller-Segel equation; growth and expansion
[note] [no recording – sorry!]
HW3 solution
L18 M, Mar 7 Spatiotemporal patterns in development I: 
Turing instability and Turing space
[note] [YouTube recording]
HW4 solution
L19 W, Mar 9 Spatiotemporal patterns in development II: [recording]
finite domains and mode selection [note];
intro to Swift-Hohenberg model and amplitude equation [note
final project (select project topic by end of Friday March 11)
  F, Mar 18
final project presentation on spatiotemporal patterns