Differential equations with delay naturally arise in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, distributed networks, heat flows, neural networks, combustion, interaction of species, microbiology, learning models, epidemiology, physiology, and many others. This book systematically investigates the stability of linear as well as nonlinear vector differential equations with delay and equations with causal mappings. It presents explicit conditions for exponential, absolute and input-to-state stabilities. These stability conditions are mainly formulated in terms of the determinants and eigenvalues of auxiliary matrices dependent on a parameter; the suggested approach allows us to apply the well-known results of the theory of matrices. In addition, solution estimates for the considered equations are established which provide the bounds for regions of attraction of steady states.

This text is designed for a first course in biological mass transport, and the material in it is presented at a level that is appropriate to advanced undergraduates or early graduate level students. Its orientation is somewhat more physical and mathematical than a biology or standard physiology text, reflecting its origins in a transport course that I teach to undergraduate (and occasional graduate) biomedical engineering students in the Whiting School of Engineering at Johns Hopkins. The audience for my cours- and presumably for this text - also includes chemical engineering undergraduates concentrating in biotechnology, and graduate students in biophysics. The organization of this book differs from most texts that at­ tempt to present an engineering approach to biological transport. What distinguishes biological transport from other mass transfer processes is the fact that biological transport is biological. Thus, we do not start with the engineering principles of mass transport (which are well presented elsewhere) and then seek biological ap­ plications of these principles; rather, we begin with the biological processes themselves, and then develop the tools that are needed to describe them. As a result, more physiology is presented in this text than is often found in books dealing with engineering applica­ tions in the life sciences.

The use of digital signal processing is ubiquitous in the field of physiology and biomedical engineering. The application of such mathematical and computational tools requires a formal or explicit understanding of physiology. Formal models and analytical techniques are interlinked in physiology as in any other field. This book takes a unitary approach to physiological systems, beginning with signal measurement and acquisition, followed by signal processing, linear systems modelling, and computer simulations. The signal processing techniques range across filtering, spectral analysis and wavelet analysis. Emphasis is placed on fundamental understanding of the concepts as well as solving numerical problems. Graphs and analogies are used extensively to supplement the mathematics. Detailed models of nerve and muscle at the cellular and systemic levels provide examples for the mathematical methods and computer simulations. Several of the models are sufficiently sophisticated to be of value in understanding real world issues like neuromuscular disease. This second edition features expanded problem sets and a link to extra downloadable material.

The development of a proper description of the living world today stands as one of the most significant challenges to physics. A variety of new experimental techniques in molecular biology, microbiol­ ogy, physiology and other fields of biological research constantly expand our knowledge and enable us to make increasingly more detailed functional and structural descriptions. Over the past decades, the amount and complexity of available information have multiplied dramatically, while at the same time our basic understanding of the nature of regulation, behavior, morphogenesis and evolution in the living world has made only modest progress. A key obstacle is clearly the proper handling of the available data. This requires a stronger emphasis on mathematical modeling through which the consistency of the adopted explanations can be checked, and general princi­ ples may be extracted. As an even more serious problem, however, it appears that the proper physical concepts for the development of a theoretically oriented biology have not hitherto been available. Classical mechanics and equilibrium thermody­ namics, for instance, are inappropriate and useless in some of the most essen­ tial biological contexts. Fortunately, there is now convincing evidence that the concepts and methods of the newly developed fields of nonlinear dynam­ ics and complex systems theory, combined with irreversible thermodynamics and far-from-equilibrium statistical mechanics will enable us to move ahead with many of these problems.