In the theory of functional differential equations with infinite delay, there are several ways to choose the space of initial functions (phase space); and diverse (duplicated) theories arise, according to the choice of phase space. To unify the theories, an axiomatic approach has been taken since the 1960's. This book is intended as a guide for the axiomatic approach to the theory of equations with infinite delay and a culmination of the results obtained in this way. It can also be used as a textbook for a graduate course. The prerequisite knowledge is foundations of analysis including linear algebra and functional analysis. It is hoped that the book will prepare students for further study of this area, and that will serve as a ready reference to the researchers in applied analysis and engineering sciences.

This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others.While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

This monograph provides a definitive overview of recent advances in the stability and oscillation of autonomous delay differential equations. Topics include linear and nonlinear delay and integrodifferential equations, which have potential applications to both biological and physical dynamic processes. Chapter 1 deals with an analysis of the dynamical characteristics of the delay logistic equation, and a number of techniques and results relating to stability, oscillation and comparison of scalar delay and integrodifferential equations are presented. Chapter 2 provides a tutorial-style introduction to the study of delay-induced Hopf bifurcation to periodicity and the related computations for the analysis of the stability of bifurcating periodic solutions. Chapter 3 is devoted to local analyses of nonlinear model systems and discusses many methods applicable to linear equations and their perturbations. Chapter 4 considers global convergence to equilibrium states of nonlinear systems, and includes oscillations of nonlinear systems about their equilibria. Qualitative analyses of both competitive and cooperative systems with time delays feature in both Chapters 3 and 4. Finally, Chapter 5 deals with recent developments in models of neutral differential equations and their applications to population dynamics. Each chapter concludes with a number of exercises and the overall exposition recommends this volume as a good supplementary text for graduate courses. For mathematicians whose work involves functional differential equations, and whose interest extends beyond the boundaries of linear stability analysis.

Privacy is an unwieldy concept that has eluded an essentialised definition despite its centrality and importance in the body of bioethics. The compilation presented in this volume represents continuing discussions on the theme of privacy in the context of genetic information. It is intended to present a wide range of expert opinion in which the notion of privacy is examined from many perspectives, in different contexts and imperatives, and in different societies, with the hope of advancing an understanding of privacy through the examination and critique of some of its evolving component concepts such as notions of what constitute the personal, the context of privacy, the significance and impact of the relational interests of others who may share the same genetic inheritance, and mechanisms for the protection of privacy (as well as of their limitations), among others. More specifically, the discussions in this volume encourages us to think broadly about privacy, as encompassing values that are entailed in the sociality of context and of relations, and also as freedom from illegitimate and excessive surveillance. A long-standing question that continues to challenge us is whether genetic information should be regarded as exceptional, as it is often perceived. A conclusion that could be derived from this volume is that while genetic information may be significant, it is not exceptionally so. The work presented in this volume underlines the continuing and growing relevance of notions of privacy to genomic science, and the need to take ownership of a genetic privacy for the future through broad, rigorous and open discussion.Contributors: Alastair V Campbell, Benjamin Capps, Jacqueline JL Chin, Oi Lian Kon, Kenji Matsui, Thomas H Murray, Nazirudin Mohd Nasir, Dianne Nicol, Anh Tuan Nuyen, Onora O'Neill, Margaret Otlowski, Yvette van der Eijk, Chunshui Wang, Ross S White.

This book looks at the theories of Volterra integral and functional equations.