∞
Dynamical Systems
Undergraduate
Definition
A dynamical system mathematically models how states evolve over time. It's expressed through differential or difference equations.
Formulas
(dx)/(dt) = f(x)
Continuous dynamical system (autonomous)
x_n+1 = f(xₙ)
Discrete dynamical system
Examples
Example 1
Solve the population growth model dP/dt = rP.
Applications
Physics
Planetary motion, pendulum
Biology
Population dynamics, ecosystem models
Economics
Business cycles, market dynamics
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