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Logistic Map Study | Complex Systems | mileswaite.net

Logistic Map Study

Study ID: 223e4567-e89b-12d3-a456-426614174111

The Logistic Map is a classic example of how simple nonlinear systems can exhibit incredibly complex—and chaotic—behavior. Each study here corresponds to a specific analysis of the map: xₙ₊₁ = r·xₙ·(1−xₙ).

System Parameters

r Min: 2.5

r Max: 4.0

Key Findings & Universal Constants

Feigenbaum δ:N/A(Known value: 4.6692...)

The Feigenbaum constant δ ≈ 4.669 is a universal number characterizing how the period-doubling bifurcations accumulate in many nonlinear systems, including the logistic map. This constant describes the ratio of successive bifurcation intervals.

Other Constants:Feigenbaum alpha (α): 2.5029078750 | Feigenbaum delta (δ): 4.6692016091

The Period-Doubling Cascade

The logistic map famously follows the period-doubling route to chaos, with regular periods doubling at predictable r values, culminating in unpredictable/chaotic outcomes.

Bifurcation Diagram

A bifurcation diagram visualizes the long-term behaviors of the logistic map as the parameter r changes, revealing fixed points, periodic orbits, and chaos.

Lyapunov Exponent Plot

The Lyapunov exponent measures sensitivity to initial conditions—positive values indicate chaos. The plot below shows how chaos emerges as r increases.

Data Export

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API Endpoints for This Study

GET /api/studies/logistic/223e4567-e89b-12d3-a456-426614174111Study details
GET /api/studies/logistic/223e4567-e89b-12d3-a456-426614174111/bifurcationBifurcation data
GET /api/studies/logistic/223e4567-e89b-12d3-a456-426614174111/feigenbaumUniversal constants