The Logistic Map and the Route to Chaos

Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.

Contenu

General and Historical Introduction.- Chaotic Growth with the Logistic Model of P.-F. Verhulst.- Pierre-François 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.