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Dynamical Systems, PDEs and Networks for Biomedical Applications: Mathematical Modeling, Analysis and Simulations

2023-02-15 Science
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Release : 2023-02-15
Genre : Science
Kind : eBook
Book Rating : 588/5 ( reviews)

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Book Synopsis Dynamical Systems, PDEs and Networks for Biomedical Applications: Mathematical Modeling, Analysis and Simulations by : André H. Erhardt

Download or read book Dynamical Systems, PDEs and Networks for Biomedical Applications: Mathematical Modeling, Analysis and Simulations written by André H. Erhardt. This book was released on 2023-02-15. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Models and Computer Simulations for Biomedical Applications

2023-09-17 Mathematics
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Release : 2023-09-17
Genre : Mathematics
Kind : eBook
Book Rating : 159/5 ( reviews)

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Book Synopsis Mathematical Models and Computer Simulations for Biomedical Applications by : Gabriella Bretti

Download or read book Mathematical Models and Computer Simulations for Biomedical Applications written by Gabriella Bretti. This book was released on 2023-09-17. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamical System Models in the Life Sciences and Their Underlying Scientific Issues

2018 Biology
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Release : 2018
Genre : Biology
Kind : eBook
Book Rating : 708/5 ( reviews)

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Book Synopsis Dynamical System Models in the Life Sciences and Their Underlying Scientific Issues by : Frederic Y. M. Wan

Download or read book Dynamical System Models in the Life Sciences and Their Underlying Scientific Issues written by Frederic Y. M. Wan. This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems

2008-12-26 Technology & Engineering
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Release : 2008-12-26
Genre : Technology & Engineering
Kind : eBook
Book Rating : 780/5 ( reviews)

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Book Synopsis Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems by : Jan Awrejcewicz

Download or read book Modeling, Simulation and Control of Nonlinear Engineering Dynamical Systems written by Jan Awrejcewicz. This book was released on 2008-12-26. Available in PDF, EPUB and Kindle. Book excerpt: 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 Delay ODE/PDE Models

2019-11-25 Medical
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Release : 2019-11-25
Genre : Medical
Kind : eBook
Book Rating : 730/5 ( reviews)

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Book Synopsis Time Delay ODE/PDE Models by : W.E. Schiesser

Download or read book Time Delay ODE/PDE Models written by W.E. Schiesser. This book was released on 2019-11-25. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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