Forecasting the evolution of complex systems is noted as one of the 10 grand challenges of
modern science. Time series data from complex systems capture the dynamic behaviors and …

Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of
complex dynamics. Utilising a pragmatic, physical approach, this self-contained book …

The book treats the theory of attractors for non-autonomous dynamical systems. The aim of
the book is to give a coherent account of the current state of the theory, using the framework …

The theory of nonautonomous dynamical systems in both of its formulations as processes
and skew product flows is developed systematically in this book. The focus is on dissipative …

This book is devoted to the asymptotic properties of solutions of stochastic evolution
equations in infinite dimensional spaces. It is divided into three parts: Markovian dynamical …

This book develops the theory of global attractors for a class of parabolic PDEs that includes
reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated …

This paper describes a free energy principle that tries to explain the ability of biological
systems to resist a natural tendency to disorder. It appeals to circular causality of the sort …

We study pullback attractors of non-autonomous non-compact dynamical systems generated
by differential equations with non-autonomous deterministic as well as stochastic forcing …

In 438 alphabetically-arranged essays, this work provides a useful overview of the core
mathematical background for nonlinear science, as well as its applications to key problems …

The existence of a pullback attractor is established for a stochastic reaction–diffusion
equation on all n-dimensional space. The nonlinearity is dissipative for large values of the …