The bifurcation pattern seen in the logistic map turns out to be universal across a wide range of dynamic systems, including systems of differential equations, and more importantly, experiments. It seems the logistic map was just the first example of a large class of systems, which led to the discovery of new constants in the universe.

► Next, Feigenbaum's renormalization analysis of period-doubling, demonstrating where the universal constants come from
   • Renormalization Theory for Dynamical ...  

► Logistic map
Introduction    • Logistic Map, Part 1: Period Doubling...  
Bifurcation diagram    • Logistic Map, Part 2: Bifurcation Dia...  
Analysis of fixed points and cycles    • Logistic Map, Part 3: Bifurcation Poi...  

► Additional background
Introduction to mappings    • Maps, Discrete Time Dynamical Systems...  
Logistic equation (1D ODE)    • Population Growth- The Logistic Model  
Lorenz map on strange attractor    • Dynamics on Lorenz Attractor | Lorenz...  
Lorenz equations introduction    • 3D Systems, Lorenz Equations Derived,...  
Definitions of chaos and attractor    • Chaotic Attractors: a Working Definit...  

► Ghosts and bottlenecks
In 1D differential equations    • Flows on the Circle | Ghosts and Bott...  
In 2D differential equations    • Bifurcations in 2D, Part 1: Introduct...  

► From 'Nonlinear Dynamics and Chaos' (online course).
Playlist https://is.gd/NonlinearDynamics

► Dr. Shane Ross, Virginia Tech professor (Caltech PhD)
Subscribe https://is.gd/RossLabSubscribe​

► Follow me on Twitter
  / rossdynamicslab  

► Course lecture notes (PDF)
https://is.gd/NonlinearDynamicsNotes

► Advanced lecture on maps from another of my courses
   • Center Manifold Theory for Maps, with...  

► Robert May's 1976 article introducing the logistic map (PDF)
https://is.gd/logisticmappaper

References:
Steven Strogatz, "Nonlinear Dynamics and Chaos", Chapter 10: One-Dimensional Maps

► Free online courses by Dr. Ross

📚Nonlinear Dynamics & Chaos
https://is.gd/NonlinearDynamics

📚Hamiltonian Dynamics
https://is.gd/AdvancedDynamics

📚Lagrangian & 3D Rigid Body Dynamics
https://is.gd/AnalyticalDynamics

📚Center Manifolds, Normal Forms, and Bifurcations
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📚Attitude Dynamics & Control
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📚3-Body Problem Orbital Mechanics
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📚Space Manifolds
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