decochators 1.0.5

Library for analysis and visualization of chaotic systems

decochators is a library to facilitate the study (visualization and analysis) of chaotic systems focused on application in CBE (Chaos-Based-Encryption) algorithms.

Structure

Class chaoticMap
│ 
├── Inherited class mth (Analysis)
│ 	│ 
│   ├── func Lyapunov
│   ├── func Kolmogorov-Sinai
│   └── func Test 0-1 (Binarized!!!)
│
└── Inherited class vwr (Visualization)
	│ 
    ├── func Draw
    ├── func Bifurcation
    └── func Test 0-1

Supported Python Versions

• Python 3.11+

Supported Chaos Systems

• One-dimensional
• Three-dimensional
  • Continuous dynamic systems
  • Discrete over time

Installing

Install or upgrade the Python bindings with pip <https://pip.pypa.io/>.

Latest official release:

pip install -U decochators

Specific version (not recommended for versions lower than 1.1.0):

pip install -U decochators==N.N.NxN

Latest official release from TestPypi:

pip install -i https://test.pypi.org/simple/ decochators

Specific version from TestPypi:

pip install -i https://test.pypi.org/simple/ decochators==N.N.NxN

Where $N \in \mathbb{Z}$ and $x \in {a, b, c, \dots, z}$, example: 1.0.4a0.

Note: you should consider using a virtual environment to create an isolated Python environment for installation.

Testing Binary Chaos Test 0-1

Important for versions lower than decochators1.1.0, mth.test01 is a binarized modified test, be careful comparing or testing complex systems.

from decochators import attach_chaos_tests
import numpy as np

@attach_chaos_tests("1d")
def logistic_step(x: float, r: float = 4.0) -> float:
    return r * x * (1 - x)

serie = logistic_step(0.1, r=3.9, N=1000, burn_in=100, seed=42)
k01 = logistic_step.mth.test01(0.1, r=3.9)

print("Results with burn-in & seed:")
print(f"Test 0-1 with the serie binarized: {k01}")

k01_vwr=logistic_step.vwr.test01(
    logistic_step.__wrapped__,
    x0=0.1,
    N=1000,
    burn_in=100,
    r=3.9
),

print(f"Complete Test 0-1: {k01_vwr}")

Calling other 1 Dimensions functions

With the same chaotic system than before:

def logistic_step(x: float, r: float = 4.0) -> float:
    return r * x * (1 - x)

Generating series

logistic_step(0.1, r=3.9, N=1000, burn_in=100, seed=42)

Lyapunov Exponent Analysis

logistic_step.mth.lyapunov(0.1, r=3.9)

Kolmorogov-Sinai Analysis

logistic_step.mth.ks(0.1, r=3.9)

Chaotic Draw Visualization

logistic_step.vwr.draw(logistic_step.__wrapped__, x0=0.3, N=250000, burn_in=100, r=4.0)

Bifurcation System Visualization

import numpy as np

param_range = np.linspace(2.5, 4.0, 300)
logistic_step.vwr.bifurcation(logistic_step.__wrapped__, x0=0.1, param_name="r", param_range=param_range, N=5000, burn_in=200, last_points=50)

Calling 3 Dimensions functions

Chaotic System sample:

def rossler_step(xyz: np.ndarray, a: float = 0.2, b: float = 0.2, c: float = 5.7) -> np.ndarray:
    x, y, z = xyz
    dt = 0.01
    dx = -y - z
    dy = x + a*y
    dz = b + z*(x - c)
    return np.array([x + dx*dt, y + dy*dt, z + dz*dt])

Lyapunov Exponent Analysis

rossler_step.mth.lyapunov([0.1,0,0])

Kolmorogov-Sinai Analysis

rossler_step.mth.ks([0.1,0,0])

Binary Test Analysis

As in 1 Dimension, 3D mth.test01 is in base of a binarized test in lower than decochatorsv1.1.0, be careful.

rossler_step.mth.test01([0.1,0,0])

Chaotic Draw Visualization

rossler_step.vwr.draw(rossler_step.__wrapped__, [0.1, 0.0, 0.0], N=10000, burn_in=500, a=0.2, b=0.2, c=5.7)

Bifurcation System Visualization

import numpy as np

rossler_step.vwr.bifurcation(
    step_func=rossler_step,
    xyz0=[0.1,0.0,0.0],
    param_name='c',
    param_range=np.linspace(4, 6, 200),
    coord=2,      # Project on Cord Z | 0=X;1=Y;2=Z
    N=2000,
    burn_in=500
)

Binary Tests Visualization

On the other hand, vwr.test01 is the completed binary test, without binarization.

rossler_step.vwr.test01(rossler_step.__wrapped__, [0.1,0.0,0.0], N=5000, burn_in=100)

---

For further explication: https://yoshlsec.github.io/cbe-blogs/ For source code: https://github.com/yoshlsec/decochators

I hope its useful, first public python module for you all ;)