Using the concepts of chaotic dynamical systems, we present an interpretation of dynamic
neural activity found in cortical and subcortical areas. The discovery of chaotic itinerancy in …

Intelligent behavior is characterized by flexible and creative pursuit of endogenously defined
goals. Intentionality is a key concept by which to link neuron and brain to goal-directed …

In this book we will study equations of the following form x= f (x, t; µ),(0.0. 1) and x↦→ g (x;
µ),(0.0. 2) with x∈ U⊂ Rn, t∈ R1, and µ∈ V⊂ Rp where U and V are open sets in Rn and …

Turbulence pervades our world, from weather patterns to the air entering our lungs. This
book describes methods that reveal its structures and dynamics. Building on the existence of …

This text provides an introduction to the exciting new developments in chaos and related
topics in nonlinear dynamics, including the detection and quantification of chaos in …

The previous edition of this text was the first to provide a quantitative introduction to chaos
and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of …

On the example of the famous Lorenz system, the difficulties and opportunities of reliable
numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz …

This book is an introduction to the theory of shadowing of approximate trajectories in
dynamical systems by exact ones. This is the first book completely devoted to the theory of …

The study of the magnetic fields of the Earth and Sun, as well as those of other planets, stars,
and galaxies, has a long history and a rich and varied literature, including in recent years a …

In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows,
with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the …