Equilibrium states and periodic behavior in dynamical systems
🎯 Hook
💡 Intuition
📚 Theory
🎮 Playground
✏️ Practice
The Road to Chaos
How does a simple equation create infinite complexity?
The answer lies in fixed points and periodic orbits - and how they lose stability.
The Population Puzzle
Imagine tracking a population that reproduces each generation according to a simple rule: next = r * current * (1 - current). What happens as we increase r?
Growth Rate (r): 2.50
r=1r=3chaosr=4
Population Over Time
Iteration Map
With r = 2.50, what do you predict for the long-term behavior?
Try it! Adjust the growth rate r and click Run Simulation to see fixed points give way to cycles and chaos!
