Chaos Classifier: Logistic Map Regime Detection via 1D CNN This model classifies time series sequences generated by the logistic map into one of three dynamical regimes:
0 → Stable (converges to a fixed point) 1 → Periodic (oscillates between repeating values) 2 → Chaotic (irregular, non-repeating behavior) The goal is to simulate financial market regimes using a controlled chaotic system and train a model to learn phase transitions directly from raw sequences.
Motivation Financial systems often exhibit regime shifts: stable growth, cyclical trends, and chaotic crashes. This model uses the logistic map as a proxy to simulate such transitions and demonstrates how a neural network can classify them.
Data Generation Sequences are generated from the logistic map equation:
[ x_{n+1} = r \cdot x_n \cdot (1 - x_n) ]
Where:
x₀ ∈ (0.1, 0.9) is the initial condition r ∈ [2.5, 4.0] controls behavior Label assignment:
r < 3.0 → Stable (label = 0) 3.0 ≤ r < 3.57 → Periodic (label = 1) r ≥ 3.57 → Chaotic (label = 2) Model Architecture A 1D Convolutional Neural Network (CNN) was used:
Conv1D → BatchNorm → ReLU × 2 GlobalAvgPool1D Linear → Softmax (via CrossEntropyLoss) Advantages of 1D CNN:
Captures local temporal patterns Learns wave shapes and jitters Parameter-efficient vs. MLP Performance Trained on 500 synthetic sequences (length = 100), test accuracy reached:
98–99% accuracy Smooth convergence Robust generalization Confusion matrix showed near-perfect stability detection and strong chaos/periodic separation Inference Example You can generate a prediction by passing an r value:
predict_regime(3.95, model, scaler, device)