https://github.com/sandyherho/kalimusada

A Python solver for the Ma-Chen financial chaotic system with sensitivity analysis and visualization.
https://github.com/sandyherho/kalimusada

chaos-theory financial-modeling nonlinear-dynamics

Last synced: 5 months ago
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A Python solver for the Ma-Chen financial chaotic system with sensitivity analysis and visualization.

• Host: GitHub
• URL: https://github.com/sandyherho/kalimusada
• Owner: sandyherho
• License: mit
• Created: 2025-11-25T04:09:48.000Z (7 months ago)
• Default Branch: main
• Last Pushed: 2025-11-25T11:01:09.000Z (7 months ago)
• Last Synced: 2025-11-28T16:51:50.918Z (7 months ago)
• Topics: chaos-theory, financial-modeling, nonlinear-dynamics
• Language: Python
• Homepage: https://pypi.org/project/kalimusada/
• Size: 18.2 MB
• Stars: 0
• Watchers: 0
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# `kalimusada`: a Python library for solving the Ma-Chen financial chaotic system

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A Python-based solver for demonstrating sensitivity to initial conditions in economic dynamics.



  



## Model

The Ma-Chen system describes financial dynamics through three coupled ordinary differential equations:

$$ \dot{x} = z + (y - a)x, \quad \dot{y} = 1 - by - x^2, \quad \dot{z} = -x - cz $$

where the state variables are:

| Variable | Description | Economic interpretation |

|:--------:|:------------|:------------------------|

| $x(t)$ | Interest rate | Cost of borrowing capital |

| $y(t)$ | Investment demand | Aggregate investment activity |

| $z(t)$ | Price index | General price level |

and the parameters are:

| Parameter | Description | Chaotic value |

|:---------:|:------------|:-------------:|

| $a$ | Savings rate | $0.9$ |

| $b$ | Investment cost coefficient | $0.2$ |

| $c$ | Demand elasticity | $1.2$ |

The solver simulates two trajectories with infinitesimal initial separation $\delta_0 \sim \mathcal{O}(10^{-5})$ to visualize exponential divergence characteristic of deterministic chaos.

## Installation

**From PyPI:**

```bash

pip install kalimusada

```

**From source:**

```bash

git clone https://github.com/sandyherho/kalimusada.git

cd kalimusada

pip install -e .

```

## Quick start

**CLI:**

```bash

kalimusada case1          # run standard chaos scenario

kalimusada --all          # run all test cases

```

**Python API:**

```python

from kalimusada import MaChenSolver, MaChenSystem

system = MaChenSystem(a=0.9, b=0.2, c=1.2)

solver = MaChenSolver()

result = solver.solve(

    system=system,

    init_A=[1.0, 2.0, 0.5],

    init_B=[1.00001, 2.0, 0.5],

    t_span=(0, 250),

    n_points=100000

)

print(f"Max divergence: {result['max_euclidean_distance']:.6f}")

```

## Features

- High-precision ODE integration (LSODA)

- Dual trajectory sensitivity analysis

- Error metrics: Euclidean distance, RMSE, log divergence

- Output formats: CSV, NetCDF, PNG, GIF

## License

MIT © Sandy H. S. Herho

## Citation

```bibtex

@software{herho2025_kalimusada,

  title   = {kalimusada: A Python library for solving the Ma-Chen financial chaotic system},

  author  = {Herho, Sandy H. S.},

  year    = {2025},

  url     = {https://github.com/sandyherho/kalimusada}

}

```