René Lozi – författare

This book presents some exceptional developments in chaotic attractor theory encompassing several new directions of research such as three-dimensional axiom A-diffeomorphisms, Shilnikov attractors, dendrites and finite graphs.The theory of chaotic attractors has experienced exceptional development over the last fifty years since the revelation of chaos in mathematics (invented by James Yorke) and symbolized by the “butterfly effect”. Relevant new results have been collected in this book, including:Some remarks on minimal sets on dendrites and finite graphs and the study of recurrence and nonwandering sets of local dendrite maps.Ramified continua as global attractors of C1- smooth self-maps of a cylinder close to skew productsChaotic behaviour of countable products of homeomorphism groups and dynamics of three-dimensional axiom A-diffeomorphisms with two-dimensional attractors and repellers.The search for invariant sets of the generalized tent map and quasi-hyperbolic regime in a certain family of 2-D piecewise linear map.Shilnikov attractors of three-dimensional flows and maps, right fractional calculus to inverse-time chaotic maps and asymptotic stability analysis and diffeomorphisms with infinitely many Smale horseshoes.The theory of chaotic attractor is also used as a core for evolutionary algorithms and metaheuristic optimizers in this volume.This book will be of great value to students and researchers in mathematics, physics, engineering, and related disciplines seeking to deepen their understanding of chaotic dynamical systems and their applications.The chapters in this book were originally published in Journal of Difference Equations and Applications.

This book offers a captivating exploration of the intersection between mathematics, chaos theory, and dynamical systems through the personal journeys of twelve renowned mathematicians and physicists from China, Europe, Russia, and the USA.The first section of the book provides an intimate look into the formative experiences and early steps of these scientists. In these life stories, the names of other famous mathematicians arise, crisscrossing all the stories in unexpected ways. The second part of the book explores the practical applications of chaotic attractors in various fields. These include chaos-based encryption in cryptography, sensor and actuator placement in Chua circuits for control systems, and chaotic dynamics in remote sensing for crop modeling. It also highlights the role of chaos theory in the development of memristors following Leon Chua’s 1971 discovery, leading to advances in nonlinear dynamics, hyperchaos, and memristor-based systems. The chapters further examine how chaos theory addresses modern challenges such as modeling COVID-19 spread using SEIR models and optimizing mobile network design, demonstrating the wide-reaching impact of chaotic systems in real-world applications.This book will be of great value to students and researchers in mathematics, physics, engineering, and related disciplines seeking to deepen their understanding of chaotic dynamical systems and their applications.This book includes a revised introduction and a new chapter. The remaining chapters were originally published in Journal of Difference Equations and Applications.

Over the past fifty years, the development of chaotic dynamical systems theory and its subsequent wide applicability in science and technology has been an extremely important achievement of modern mathematics. Chaotic attractors are not a fleeting curiosity, and their continued study is important for the progress of mathematics.This book collects several of the new relevant results on the most important of them: the Lozi, Hénon and Belykh attractors. Existence proofs for strange attractors in piecewise-smooth nonlinear Lozi-Hénon and Belykh maps are given. Generalization of Lozi map in higher dimensions, Markov partition or embedding into the 2D border collision normal form of this map are considered. K-symbol fractional order discrete-time and relationship between this map and maxtype difference equations are explored. Statistical self-similarity, control of chaotic transients, and target-oriented control of Hénon and Lozi attractors are presented. Controlling chimera and solitary states by additive noise in networks of chaotic maps, detecting invariant expanding cones for generating word sets to identify chaos in piecewise-linear maps, and studying border collision bifurcations in a piecewise linear duopoly model complete this book.This book is an essential companion for students and researchers in mathematics, physics, engineering, and related disciplines seeking to deepen their understanding of chaotic dynamical systems and their applications.The chapters in this book were originally published in Journal of Difference Equations and Applications.

This book covers in an integrated way the foundations and practical applications on modern chaos-based cryptographic systems. It is aimed at a wide audience: PhD students, engineers in initial training, Master 2 students, specializing in data security and complex networks (satellites, mobile telephony, Internet, Internet of Things, etc.), computer science or in other related specialties (informatics, electronics and mathematics). It is also intended for professionals and trainers, guiding them in the design of new cryptographic systems and the construction of their training courses.First, it provides all the necessary concepts for understanding the principle of standard and chaos-based cryptography. Then, it introduces the elements of chaos theory. Subsequently, it deals with the design, hardware (on Field Programmable Gate Array) and software implementations as well as performance analysis of practical chaos-based cryptographic systems: pseudo-random number generators of chaotic sequences (PRNGs-CS), chaos-based stream and block ciphers, chaos-based hash functions and chaos-based authenticated encryptions.

This book presents contributions related to new research results presented at the 27th International Conference on Difference Equations and Applications, ICDEA 2022, that was held at CentraleSupélec, Université Paris-Saclay, France, under the auspices of the International Society of Difference Equations (ISDE), July 18–22, 2022.

This book presents contributions related to new research results presented at the 27th International Conference on Difference Equations and Applications, ICDEA 2022, that was held at CentraleSupélec, Université Paris-Saclay, France, under the auspices of the International Society of Difference Equations (ISDE), July 18–22, 2022.

This proceedings volume gathers selected and invited contributions presented at the 29th International Conference on Difference Equations and Applications (ICDEA), held in Paris, France, from June 24 to 28, 2024. Papers in this volume cover topics in the theory and applications of difference equations and discrete dynamical systems in fields as diverse as mathematical economics, mathematical biology, and others, offering a glimpse of the state of the art in these fields.Organized by the International Society of Difference Equations (ISDE) since 1994, the ICDEA has become an invaluable opportunity for experts and students worldwide to share their findings and foster avenues of cooperation. Volumes from previous iterations of ICDEA are also available from Springer.

The book discusses essential topics in industrial and applied mathematics such as image processing with a special focus on medical imaging, biometrics and tomography. Applications of mathematical concepts to areas like national security, homeland security and law enforcement, enterprise and e-government services, personal information and business transactions, and brain-like computers are also highlighted. These contributions – all prepared by respected academicians, scientists and researchers from across the globe – are based on papers presented at the international conference organized on the occasion of the Silver Jubilee of the Indian Society of Industrial and Applied Mathematics (ISIAM) held from 29 to 31 January 2016 at Sharda University, Greater Noida, India. The book will help young scientists and engineers grasp systematic developments in those areas of mathematics that are essential to properly understand challenging contemporary problems.