Dynamical Systems Explorer

Explore the fascinating world of dynamical systems, from simple linear equations to complex chaotic phenomena. Click on any category to discover the systems and phenomena within.

Understanding Dynamical Systems
Dynamical systems are mathematical models that describe how systems evolve over time. They are classified by their linearity and the number of variables involved.

Linear Systems

Predictable, well-understood systems where small changes lead to proportional effects.

Nonlinear Systems

Complex systems where small changes can lead to dramatically different outcomes.

Linear
n = 1
Growth, decay, or equilibrium

4 systems including Exponential growth, RC circuit...

Linear
n = 2
Oscillations

5 systems including Linear oscillator, Mass and spring...

Linear
n ≥ 3
Engineering Systems

4 systems including Civil engineering structures, Electrical engineering...

Linear
n >> 1
Collective phenomena

6 systems including Coupled harmonic oscillators, Solid-state physics...

Linear
Continuum
Waves and patterns

8 systems including Elasticity, Wave equations...

Nonlinear
n = 1
Fixed points and bifurcations

6 systems including Fixed points, Bifurcations...

Nonlinear
n = 2
Complex dynamics

8 systems including Pendulum, Anharmonic oscillators...

Nonlinear
n ≥ 3
Chaos and complexity

8 systems including Strange attractors (Lorenz), 3-body problem (Poincaré)...

Nonlinear
n >> 1
Collective nonlinear phenomena

19 systems including Coupled nonlinear oscillators, Lasers, nonlinear optics...

Nonlinear
Continuum
Spatio-temporal complexity

22 systems including Nonlinear waves, Plasmas...

Stochastic
stochastic
Stochastic Systems

7 systems including Stochastic differential equations, Jump processes...

Frontier
The Frontier
The Frontier

10 systems including Practical uses of chaos, Quantum chaos...