Explore pattern formation in biology through this comprehensive lecture by Vijaykumar Krishnamurthy from the International Centre for Theoretical Sciences. Delve into linear stability analysis, fixed points, and underdamped systems before examining a general setup for dynamical systems. Investigate two-variable systems and their role in pattern formation, using real-world examples to illustrate key concepts. Learn about homogeneous steady-states, the Ginzburg-Landau equation, and perturbation theory. Analyze growth rates through spectral analysis and discover the Swift-Hohenberg model. Conclude with a Q&A session to reinforce understanding of these complex biological phenomena.
Overview
Syllabus
Pattern Formulation in Biology Lecture 2
Linear Stability Analysis
Fixed points
Underdamped
General setup
Explore the dynamical system
Two Variables
Pattern formation
Examples
Homogeneous Steady-State
Ginzburg-Landau equation
Assuming homogeneous steady-state
Perturbation
Spectrum: Growth rate
Swift-Hohenberg
Q&A
Taught by
International Centre for Theoretical Sciences
