Table 2 The Chaos Decision Tree Algorithm classified non-biological simulations as stochastic, periodic, or chaotic with high accuracy. These simulated systems include strange non-chaotic attractors (SNAs), linear stochastic processes, and nonlinear stochastic processes, all of which are classically difficult to distinguish from chaos.
Measurement noise level (% of std. dev.) | |||||
|---|---|---|---|---|---|
System | 0% | 10% | 20% | 30% | 40% |
Cubic map50 (chaotic) | 100/100 | 100/100 | 100/100 | 100/100 | 100/100 |
Cubic map50 (periodic) | 100/100 | 100/100 | 100/100 | 100/100 | 100/100 |
Cubic map50 (SNA HH) | 100/100 | 100/100 | 100/100 | 100/100 | 100/100 |
Cubic map50 (SNA S3) | 100/100 | 100/100 | 100/100 | 100/100 | 0/100 |
GOPY map51 (SNA) | 100/100 | 100/100 | 100/100 | 99/100 | 14/100 |
Logistic map52 (chaotic) | 100/100 | 100/100 | 100/100 | 100/100 | 100/100 |
Logistic map52 (periodic) | 100/100 | 100/100 | 100/100 | 100/100 | 100/100 |
Lorenz system53 (chaotic) | 100/100 | 100/100 | 97/100 | 82/100 | 36/100 |
Generalized Hénon map54 (hyperchaotic) | 100/100 | 100/100 | 100/100 | 100/100 | 93/100 |
Freitas map55 (nonlinear stochastic) | 78/100 | 83/100 | 98/100 | 98/100 | 74/100 |
Noise-driven sine map55 (nonlinear stochastic) | 55/100 | 3/100 | 22/100 | 5/100 | 78/100 |
Bounded random walk56 (nonlinear stochastic) | 100/100 | 97/100 | 59/100 | 95/100 | 100/100 |
Cyclostationary process57 (linear stochastic) | 99/100 | 100/100 | 99/100 | 100/100 | 100/100 |
ARMA process (linear stochastic) | 85/100 | 98/100 | 99/100 | 99/100 | 100/100 |
Trended random walk (linear stochastic) | 100/100 | 89/100 | 90/100 | 98/100 | 100/100 |
Random walk (linear stochastic) | 100/100 | 98/100 | 100/100 | 100/100 | 100/100 |
Violet noise58 (linear stochastic) | 99/100 | ||||
Blue noise58 (linear stochastic) | 100/100 | ||||
White noise58 (linear stochastic) | 100/100 | ||||
Pink noise58 (linear stochastic) | 100/100 | ||||
Red noise58 (linear stochastic) | 100/100 | ||||
