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.
Tassos Bountis is Professor Emeritus of the Department of Mathematics, University of Patras, Greece. He has been the director of the Center for Research and Application of Nonlinear Systems of the University of Patras, and the Laboratory of Nonlinear Systems and Applied Analysis. In 2014 he was elected Corresponding Member of the Academy of Athens in the chair of complex systems. He was the recipient of the 2014 Charles Hermite Science Ambassador Award of Saar/Germany and the 2009 Academy of Athens Award for Dynamical Systems. In 2015 he was elected member of the European Academy of Science and Arts, at Salzburg, Austria.
