Mathematical modelling and computer simulations are playing a crucial role in the solution of the complex problems arising in the field of biomedical sciences and provide a support to clinical and experimental practices in an interdisciplinary framework. Indeed, the development of mathematical models and efficient numerical simulation tools is of key importance when dealing with such applications. Moreover, since the parameters in biomedical models have peculiar scientific interpretations and their values are often unknown, accurate estimation techniques need to be developed for parameter identification against the measured data of observed phenomena. In the light of the new challenges brought by the biomedical applications, computational mathematics paves the way for the validation of the mathematical models and the investigation of control problems. The volume hosts high-quality selected contributions containing original research results as well as comprehensive papers and survey articles including prospective discussion focusing on some topical biomedical problems. It is addressed, but not limited to: research institutes, academia, and pharmaceutical industries.

Broadly speaking, there are two general approaches to teaching mathematical modeling: 1) The case study approach focusing on different specific modeling problems familiar to the particular author, and 2) The methods approach teaching some useful mathematical techniques accessible to the targeted student cohort with different models introduced to illustrate the application of the methods taught. The goal and approach of this new text differ from these two conventional approaches in that its emphasis is on the scientific issues that prompt the mathematical modeling and analysis of a particular phenomenon. For example, in the study of a fish population, we may be interested in the growth and evolution of the population, whether the natural growth or harvested population reaches a steady state (equilibrium or periodically changing) population in a particular environment, is a steady state stable or unstable with respect to a small perturbation from the equilibrium state, whether a small change in the environment would lead to a catastrophic change, etc. Each of these scientific issues requires the introduction of a different kind of model and a different set of mathematical tools to extract information about the same biological organisms or phenomena.Volume I of this three volume set limits its scope to phenomena and scientific issues that can be modeled by ordinary differential equations (ODE) that govern the evolution of the phenomena with time. The scientific issues involved include evolution, equilibrium, stability, bifurcation, feedback, optimization and control. Scientific issues such as signal and wave propagation, diffusion, and shock formation pertaining to phenomena involving spatial dynamics are to be modeled by partial differential equations (PDE) and will be treated in Volume II. Scientific issues involving randomness and uncertainty are deferred to Volume III.

This volume contains the invited papers presented at the 9th International Conference "Dynamical Systems — Theory and Applications" held in Lódz, Poland, December 17-20, 2007, dealing with nonlinear dynamical systems. The conference brought together a large group of outstanding scientists and engineers, who deal with various problems of dynamics encountered both in engineering and in daily life. Topics covered include, among others, bifurcations and chaos in mechanical systems; control in dynamical systems; asymptotic methods in nonlinear dynamics; stability of dynamical systems; lumped and continuous systems vibrations; original numerical methods of vibration analysis; and man-machine interactions. Thus, the reader is given an overview of the most recent developments of dynamical systems and can follow the newest trends in this field of science. This book will be of interest to to pure and applied scientists working in the field of nonlinear dynamics.

Time delayed (lagged) variables are an inherent feature of biological/physiological systems. For example, infection from a disease may at first be asymptomatic, and only after a delay is the infection apparent so that treatment can begin. Thus, to adequately describe physiological systems, time delays are frequently required and must be included in the equations of mathematical models. The intent of this book is to present a methodology for the formulation and computer implementation of mathematical models based on time delay ordinary differential equations (DODEs) and partial differential equations (DPDEs). The DODE/DPDE methodology is presented through a series of example applications, particularly in biomedical science and engineering (BMSE). The computer-based implementation of the example models is explained with routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, for example, no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The DPDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The example applications can first be executed to confirm the reported solutions, then extended by variation of the parameters and the equation terms, and even the formulation and use of alternative DODE/DPDE models.

Focused on recent advances, this book covers theoretical foundations as well as various applications. It presents modern mathematical modeling approaches to the qualitative and numerical analysis of solutions for complex engineering problems in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by an international team of respected authors bridge the gap between abstract mathematical approaches, such as applied methods of modern analysis, algebra, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems on the one hand, and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. As such, the book will be of interest to mathematicians and engineers working at the interface of these fields.

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then is that they can't see the problem. one day, perhaps you will find the final question. G.K. Chesterton. The Scandal of Father Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, cod ing theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.