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Entropy in Dynamic Systems

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ISBN: 9783039216161 9783039216178 Year: Pages: 172 DOI: 10.3390/books978-3-03921-617-8 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.

Topological Groups. Advances, Surveys, and Open Questions

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ISBN: 9783038976448 Year: Pages: 160 DOI: 10.3390/books978-3-03897-645-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-03-08 11:42:05
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Following the tremendous reception of our first volume on topological groups called ""Topological Groups: Yesterday, Today, and Tomorrow"", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Well-known researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.

Dynamical Models of Biology and Medicine

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ISBN: 9783039212170 9783039212187 Year: Pages: 294 DOI: 10.3390/books978-3-03921-218-7 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Biology
Added to DOAB on : 2019-12-09 11:49:15
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Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicine

Keywords

hemodynamic model --- microcirculation load --- liquid-solid-porous media seepage coupling --- 2-combination --- graphical representation --- cell-based vector --- numerical characterization --- phylogenetic analysis --- intraguild predation --- random perturbations --- persistence --- stationary distribution --- global asymptotic stability --- quorum sensing --- chemostat --- mathematical model --- differential equations --- delay --- bifurcations --- dynamical system --- numerical simulation --- predator-prey model --- switched harvest --- limit cycle --- rich dynamics --- algae growth models --- uncertainty quantification --- asymptotic theory --- bootstrapping --- model comparison tests --- Raphidocelis subcapitata --- Daphnia magna --- spotting --- wildfire --- transport equations --- spotting distribution --- obesity --- mechano-electrochemical model --- articular cartilage --- cartilage degeneration --- cartilage loading --- optimal control --- hepatitis B --- delay differential equations (DDE) --- immune response --- drug therapy --- dynamic model --- flocculation --- global stability --- uniform persistence --- epidermis --- mathematical model --- bacterial inflammation --- bacterial competition --- chronic myeloid leukemia --- tyrosine kinase inhibitors --- immunomodulatory therapies --- combination therapy --- equilibrium points --- mathematical modeling --- prostate cancer --- androgen deprivation therapy --- data fitting --- generalized pseudo amino acid composition --- numerical characterization --- phylogenetic analysis --- identification of DNA-binding proteins --- n/a

New Trends in Differential and Difference Equations and Applications

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ISBN: 9783039215386 9783039215393 Year: Pages: 198 DOI: 10.3390/books978-3-03921-539-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:15
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This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.

Keywords

Legendre wavelets --- collocation method --- three-step Taylor method --- asymptotic stability --- time-dependent partial differential equations --- non-instantaneous impulses --- Caputo fractional derivative --- differential equations --- state dependent delays --- lipschitz stability --- limit-periodic solutions --- difference equations --- exponential dichotomy --- strong nonlinearities --- effective existence criteria --- population dynamics --- discrete Lyapunov equation --- difference equations --- Hilbert space --- dichotomy --- exponential stability --- ?-Laplacian operator --- mean curvature operator --- heteroclinic solutions --- problems in the real line --- lower and upper solutions --- Nagumo condition on the real line --- fixed point theory --- coupled nonlinear systems --- functional boundary conditions --- Schauder’s fixed point theory --- Arzèla Ascoli theorem --- lower and upper solutions --- first order periodic systems --- SIRS epidemic model --- mathematical modelling --- Navier–Stokes equations --- global solutions --- regular solutions --- a priori estimates --- weak solutions --- kinetic energy --- dissipation --- Bäcklund transformation --- Clairin’s method --- generalized Liouville equation --- Miura transformation --- Korteweg-de Vries equation --- second-order differential/difference/q-difference equation of hypergeometric type --- non-uniform lattices --- divided-difference equations --- polynomial solution --- integro-differentials --- Sumudu decomposition method --- dynamical system

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english (4)


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2019 (4)