Nonlinear science

This book provides a comprehensive exploration of Mean Field Games (MFG) theory, a mathematical framework for modeling the collective behavior of rational agents in complex systems.

This book delves into semilinear evolution equations, impulsive differential equations, and integro-differential equations with different types of delay.

Fractional evolution equations describe various complex and nonlocal systems with memory.

Fractional evolution equations describe various complex and nonlocal systems with memory.

Many nonlinear systems around us can generate a very complex and counter-intuitive dynamics that contrasts with their simplicity, but their understanding requires concepts that are outside the basic training of most science students.

The book concerns with solving about 650 ordinary and partial differential equations.

Many nonlinear systems around us can generate a very complex and counter-intuitive dynamics that contrasts with their simplicity, but their understanding requires concepts that are outside the basic training of most science students.

The goal of this book is to provide a mathematical perspective on some key elements of the so-called deep neural networks (DNNs).

The goal of this book is to provide a mathematical perspective on some key elements of the so-called deep neural networks (DNNs).

This book delves into semilinear evolution equations, impulsive differential equations, and integro-differential equations with different types of delay.

This is the fourth conference on "e;Supersymmetry and Perturbation Theory"e; (SPT 2002).

This penultimate volume contains numerous original, elegant, and surprising results in 1-dimensional cellular automata.

Master structural dynamics with this self-contained textbook, with key theoretical concepts explained via real-world applications.

This book is the third volume of lecture notes from summer schools held in the small village of Peyresq (France).

Science Sifting is designed primarily as a textbook for students interested in research and as a general reference book for existing career scientists.

In 1971, Leon O.

The modern world is complex beyond human understanding and control.

The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets.

In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena.

This book is devoted to the study of boundary value problems for nonlinear ordinary differential equations and focuses on questions related to the study of nonlinear interpolation.

This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time.

The main goal is to offer to readers a panorama of recent progress in nonlinear physics, complexity and transport with attractive chapters readable by a broad audience.

The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations.

The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory.

This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations.

This unique book aims to treat a class of nonlinear waves that are reflected from the boundaries of media of finite extent.

In this Element, the authors consider fully discretized p-Laplacian problems (evolution, boundary value and variational problems) on graphs.

Investigates new models of nonlinear flows, how they can be approximated and linearized, based on Koopman theory analysis.

Our book presents a unique and original viewpoint on natural and engineered systems.

This book presents a projector analysis of dynamic systems on time scales.

Maximally subelliptic partial differential equations (PDEs) are a far-reaching generalization of elliptic PDEs.

Maximally subelliptic partial differential equations (PDEs) are a far-reaching generalization of elliptic PDEs.

This book is devoted to the study of boundary value problems for nonlinear ordinary differential equations and focuses on questions related to the study of nonlinear interpolation.

This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time.

The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations.

This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations.

This Workshop in nonlinear dynamics and mathematical physics, organized by the Italian Nuclear Energy Agency (ENEA) in Bologna, is intended to give an updated overview of modern trends in the field of nonlinear dynamics with emphasis on applications to physics, quantum theory, plasma physics and fluid dynamics, optics and electrodynamics, computer simulation and neural networks.

During the last couple of years, fractals have been shown to represent the common aspects of many complex processes occurring in an unusually diverse range of fields including biology, chemistry, earth sciences, physics and technology.

Every reader will find something of interest in this book - from superdiffusion of the ocean surface to fetal heartbeats, from solar wind to the wearing-out of tools, from radioactive contamination to texture analysis, from image rendering to neural developments.

Wave or weak turbulence is a branch of science concerned with the evolution of random wave fields of all kinds and on all scales, from waves in galaxies to capillary waves on water surface, from waves in nonlinear optics to quantum fluids.

This book concentrates mainly on the theorem of existence of periodic orbits for higher dimensional analogs of Twist maps.

This book deals with the investigation of global attractors of nonlinear dynamical systems.

Cellular automata provide one of the most interesting avenues into the study of complex systems in general, as well as having an intrinsic interest of their own.

The present collection of reprints covers the main contributions of David Ruelle, and coauthors, to the theory of chaos and its applications.

About one and a half decades ago, Feigenbaum observed that bifurcations, from simple dynamics to complicated ones, in a family of folding mappings like quadratic polynomials follow a universal rule (Coullet and Tresser did some similar observation independently).