This repository implements a high-performance Stochastic Differential Equation (SDE) solver and a Monte Carlo simulation engine.

While the system is robust enough to handle generic multi-dimensional SDEs, it is currently demonstrated on a highly non-linear 5D biophysical system (CA1 Pyramidal Cell Model). By introducing multiplicative noise (square-root diffusion) into the slow variables, we quantify how stochastic fluctuations degrade the temporal reliability of the system—a framework mathematically analogous to stochastic volatility modeling in quantitative finance.

Unlike monolithic scripts, this engine separates the numerical solver from the business logic:

• core/sde_solvers.py: The mathematical heart. Implements the Euler-Maruyama integration scheme with generalized boundary-clipping protection for robust probability/conductance tracking.
• models/ca1_pyramidal.py: The payload. Contains the complex deterministic drift and stochastic diffusion tensors of the 5D system.
• utils/signal_processing.py: Event-driven analysis tools for peak detection and Inter-Burst Interval (IBI) extraction.
• run_parameter_sweep.py: Exploratory parameter sweep engine. Conducts high-resolution sensitivity analysis to identify dynamic bifurcation points (e.g., the exact threshold for periodic bursting) prior to stochastic testing.
• experiments/01_feature_knockout_analysis.py: Deterministic ablation studies (Factor Knockout Tests) isolating the precise systemic contributions of specific driving forces.
• main_monte_carlo.py: The pipeline. Executes 50 independent Monte Carlo paths with memory-caching optimization to reduce redundant computation during statistical aggregation.

Prior to stochastic evaluation, systematic virtual knockouts and parameter tuning were conducted. This confirmed that bursting is an emergent property requiring strict balance between modulatory drivers (e.g., $g_M$, $g_{NaP}$) and core excitability (e.g., $g_{Na}$).

We utilized the Coefficient of Variation (CV) of inter-burst intervals to measure system reliability. Results show a distinct plateau effect in timing degradation as the diffusion coefficient ($\sigma_z$) increases.

Figure: Tail-risk and reliability degradation under varying intrinsic noise intensities.

# 1. Clone the repo
git clone [https://github.com/WuYefan77/Stochastic-Dynamics-Engine.git](https://github.com/WuYefan77/Stochastic-Dynamics-Engine.git)

# 2. Install dependencies
pip install -r requirements.txt

# 3. Fire up the Monte Carlo engine
python main_monte_carlo.py