Chaos, Fractals and Complexity

This volume of proceedings contains research results within the framework of the fields of Chaos, Fractals and Complexity, written by experienced professors, young researchers, and applied scientists. It includes reviews of the fields, which are presented in an educational way for the widest possible audience, analytical results, computer simulations and experimental evidence, focusing on mathematical modelling. The papers presented here are selected from lectures given at the 28th Summer School Dynamical Systems and Complexity , July 18 27, 2022. Topics cover applications of complex systems in Neuroscience, Biology, Photonics, Seismology, Meteorology, and more broadly Physical and Engineering systems. The summer school has a long history, which began at the University of Patras in 1987 and continues with great success to this day. The original main purpose was to introduce young students and researchers of Greece to a new science that emerged several decades ago and continues to grow internationally at an ever increasing rate around the world.

Diffusion without Spreading of a Wave Packet in Nonlinear Random Models.- Nonlinear Phenomena Shaping the Structure of Spiral Galaxies.- Phase Space Transport and Dynamical Matching in a Caldera-type Hamiltonian System.- Building Blocks of Spiral Arms.- Ordered and Chaotic Bohmian Trajectories.- Introduction to Quantum Chaos of Generic Systems.- Dynamics and Statistics of Weak Chaos in a 4-Dimensional Map.- Multifractal Analysis of SEM images of Multiphase Materials: The Case of OPC Clinker.- Fractal Dimensional Analysis for Retinal Vascularization Images in Retinitis Pigmentosa: a Pilot Study.- Extending the Bayesian Framework from Information to Action.- Fokas on Medical Imaging: Analytic Reconstructions for Emission Tomography.- Inverse EEG problem, Minimization and Numerical Solutions.- Travelling Waves in Flowing Sand: The Dynamical Systems Approach.- Identifying Discrete Breathers Using Convolutional Neural Networks.- Subthreshold Oscillations in Multiplex Leaky Integrate-and-Fire Networks with Nonlocal Interactions.- Networks' Modulation: How Different Structural Network Properties affect the Global Synchronization of Coupled Kuramoto Oscillators.- Neural Correlates of Human-Machine Trust in Autonomous Vehicles.- High-Order Localized Wave Solutions of the New (3+1)-Dimensional Kadomtsev-Petviashvili Equation.- Progress in Initial-Boundary Value Problems for Nonlinear Evolution Equations and the Fokas Method.- Instabilities of Linear Evolution PDEs via the Fokas Method.- Fokas Diagonalization.- A Novel Difference-Integral Equation Satisfied Asymptotically by the Riemann Zeta Function.- The Role of Periodicity in the Solution of Third Order Boundary Value Problems.- The Fokas Method for the Well-Posedness of Nonlinear Dispersive Equations in Domains with a Boundary.- Athanassios Fokas: A Renaissance Scientist.