Catalog
Continuous flows
ODE-based dynamical systems. Each entry includes the defining equations, classical parameter values, the chaotic regime, and Lyapunov data where available.
Canonical chaotic ODEs
Lorenz, Rössler, Chen, Lü, Sprott family.
- Lorenz '63dim 3
Edward Lorenz's 1963 truncation of atmospheric convection.
- Rösslerdim 3
Otto Rössler's 1976 minimal chaotic ODE: only one nonlinearity (the xz product).
- Chen systemdim 3
Discovered by Guanrong Chen (1999).
- Lü systemdim 3
Jinhu Lü (2002) constructed this system as a bridge between Lorenz and Chen: it interpolates topologically between the two as parameters vary..
- Chua's circuitdim 3
Leon Chua's 1983 nonlinear circuit, the first physically realised chaotic electronic system.
- Sprott systems A-Sdim 3
Julien Sprott's 1994 enumeration of 19 simple chaotic flows: each with quadratic or piecewise-linear nonlinearity and minimal complexity.
Hyperchaotic
≥ 4-D systems with two or more positive Lyapunov exponents.
Delay-differential
Memory terms produce infinite-dimensional state spaces.
Driven oscillators & pendula
Duffing, Van der Pol, double pendulum.
- Duffing oscillatordim 3
Driven, damped, cubic-restoring oscillator.
- Van der Pol oscillatordim 3
Nonlinear relaxation oscillator.
- Double pendulumdim 4
The simplest mechanical system that exhibits chaotic motion.
- Kuramoto coupled oscillatorsdim ∞
N globally coupled phase oscillators with frequencies ω_i drawn from some distribution.
Neuron models
Bursting, spiking, excitability.
Chemical reactions
Belousov-Zhabotinsky and reductions.