The logistic map and the route to chaos : from the beginnings to modern applications

General and Historical Introduction.- Chaotic Growth with the Logistic Model of P.-F. Verhulst.- Pierre-Francois Verhulst's Final Triumph.- Limits to Success. The Iron Law of Verhulst.- Recurrent Generation of Verhulst Chaos Maps at Any Order and Their Stabilization Diagram by Anticipative Control.- Coherence in Complex Networks of Oscillators.- Growth of Random Sequences.- Life Relevant Physics.- Logistic Population Growth and Beyond: The Influence of Advection and Nonlocal Effects.- Predator-Prey Encounters Studied as Relative Particle Diffusion.- Extinction Dynamics in Lotka-Volterra Ecosystems on Evolving Networks.- Exact Law of Live Nature.- Manifestation of Chaos in Real Complex Systems: Case of Parkinson's Disease.- Monte Carlo Simulations of Ageing and Speciation.- Econophysics.- Influence of Information Flow in the Formation of Economic Cycles.- Logistic Function in Large Financial Crashes.- Agent Based Approaches to Income Distributions and the Impact of Memory.- Condensed Matter.- Agglomeration/Aggregation and Chaotic Behaviour in d-Dimensional Spatio-Temporal Matter Rearrangements Number-Theoretic Aspects.- A Chaos and Fractal Dynamic Approach to the Fracture Mechanics.- Nonlinear Dynamics and Fractal Avalanches in a Pile of Rice.- Miscellaneous.- A Recent Appreciation of the Singular Dynamics at the Edge of Chaos.- Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?.- On the Prediction of Chaos in the Restricted Three-Body Problem.- Order and Chaos in Some Hamiltonian Systems of Interest in Plasma Physics.