Any persisting collection of agents that interact with each other and feedback on their environment face the same problem: how to cope with fluctuations while maintaining long-term integrity. This is true whether the collection of agents refers to stem cells undergoing differentiation during development, species coexisting in an ecosystem, or traders maximizing profit in future markets. I call these ecologies. I try to escape the curse of reification, and value substance over form. This lab focuses on:
How systems avoid vanishing away while flowing in a permanently transient state.
Snapshot attractor of a seasonally forced predator and prey system (Rosenzweig-MacArthur, ε = 0.8, period 10): 500 populations driven by the same seasons forget where they started and gather on one chaotic set that keeps changing shape.
How interactions between agents and their environment shape persistence.
Predator and prey system under weak seasonal forcing (ε = 0.1) with a period of 32.7, 1.62 times the natural cycle of 20.2: orbits wind on an invariant torus, quasiperiodic with rotation number 0.607.
The ability of systems to maintain integrity amidst fluctuations.
Phase portrait of the predator and prey system below the Hopf point (K = 3 < 3.75): every 120 time units a pulse removes 70 percent of the prey, and the ensemble spirals back to coexistence, its displacement shrinking by a factor e every 40 time units (eigenvalues −0.025 ± 0.435i).
If you want a motto for the lab, keep this in mind:
Everything is moving
