Nonlinear Dynamics in an Age of Heuristic Science

Explore nonlinear dynamics through a combinatorial topology framework in this 59-minute lecture by Konstantin Mischaikow. Delve into a new approach to discussing nonlinear dynamics, motivated by challenges in systems and synthetic biology. Examine the relationship between this combinatorial approach and classical dynamics, and discover its computational efficiency. Learn about key concepts such as cell complexes, lattice of closed subchains, Conley Index, and compact metric spaces. Investigate modeling techniques using step functions and explore theoretical aspects including singularity, cost, and cusp bifurcations. Gain insights into the sheath structure and engage with questions that bridge the gap between traditional and modern approaches to nonlinear dynamics.

Introduction
Motivation for this seminar
Different definition of dynamics
From order theory
Cell complex
Lattice of closed subchains
Dynamics
Conley Index
Compact Metric Space
Modeling
Step Functions
Summary
General Theory
Engineering 101
Gamma
Dynamical Dynamics
Theorems
Singularity bifurcation
Cost bifurcation
Cusp bifurcation
Questions
The sheath structure