Ever since the pioneering work of Hodgkin and Huxley, biological neuron models have
consisted of ODEs representing the evolution of the transmembrane voltage and the …

The ability of nonlinear dynamical systems to process incoming information is a key problem
of many fundamental and applied sciences. Information processing by computation with …

The dynamics of realistic Hamiltonian systems has unusual microscopic features that are
direct consequences of its fractional space-time structure and its phase space topology. The …

The idea that cognitive activity can be understood using nonlinear dynamics has been
intensively discussed at length for the last 15 years. One of the popular points of view is that …

Over the last four decades there has been extensive development in the theory of dynamical
systems. This book aims at a wide audience where the first four chapters have been used for …

Our goal in this paper is to review the existing literature on homoclinic and heteroclinic
bifurcation theory for flows. More specifically, we shall focus on bifurcations from homoclinic …

The book aims to provide a global perspective of this theory and make it easier for the
reader to digest the growing literature on this subject. This is not the first book on the subject …

Robustness and reproducibility of sequential spatio-temporal responses is an essential
feature of many neural circuits in sensory and motor systems of animals. The most common …

A simple and transparent example of a nonautonomous flow system with a hyperbolic
strange attractor is suggested. The system is constructed on the basis of two coupled van …

Robust chaos is defined by the absence of periodic windows and coexisting attractors in
some neighborhoods in the parameter space of a dynamical system. This unique book …