The study of high critical temperature superconductors (HTS) is one of the most prominent research subjects in solid state science. An understanding of the role of fluctuations is also believed to be necessary in advance of technological applications, since the fluctuations may destroy the superconducting state. The discussions focus on: superconducting fluctuations in the vicinity of the critical transitions; superconductivity fluctuations near the percolation transition; and fluctuations of the vortex lattice at the lattice melting temperature. The effects of fluctuations on static properties and on electrical and thermal transport, properties in the ab plane and along the c axis, the effect of a magnetic field on phenomena, specifically in layered compounds are still undecided. The effect of a magnetic field is still not clear. Specific fluctuations of the vortex lattice in HTS ceramics as compared to conventional superconductors are still intensely debated.

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.