Deterministic, Stochastic and Thermodynamic Modelling of some Interacting Species

Deterministic, Stochastic and Thermodynamic Modelling of some Interacting Species

Author: Guruprasad Samanta

Publisher: Springer Nature

Published: 2021-11-24

Total Pages: 188

ISBN-13: 9811663122

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This book presents the understanding of how the different forms of regulatory mechanisms, like birth and death, competition, consumption and the like, result in changes in the stability and dynamics of ecological systems. It deals with a profound and unique insight into the mathematical richness of basic ecological models. Organised into eight chapters, the book discusses the models of mathematical ecology, the dynamical models of single-species system in a polluted environment, the dynamical behaviour of different nonautonomous two species systems in a polluted environment, the influence of environmental noise in Gompertzian and logistic growth models, stability behaviour in randomly fluctuating versus deterministic environments of two interacting species, stochastic analysis of a demographic model of urbanization and stability behaviour of a social group by means of loop analysis, thermodynamic criteria of stability and stochastic criteria of stability. The book will be useful to the researchers and graduate students who wish to pursue research in mathematical ecology.


Book Synopsis Deterministic, Stochastic and Thermodynamic Modelling of some Interacting Species by : Guruprasad Samanta

Download or read book Deterministic, Stochastic and Thermodynamic Modelling of some Interacting Species written by Guruprasad Samanta and published by Springer Nature. This book was released on 2021-11-24 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the understanding of how the different forms of regulatory mechanisms, like birth and death, competition, consumption and the like, result in changes in the stability and dynamics of ecological systems. It deals with a profound and unique insight into the mathematical richness of basic ecological models. Organised into eight chapters, the book discusses the models of mathematical ecology, the dynamical models of single-species system in a polluted environment, the dynamical behaviour of different nonautonomous two species systems in a polluted environment, the influence of environmental noise in Gompertzian and logistic growth models, stability behaviour in randomly fluctuating versus deterministic environments of two interacting species, stochastic analysis of a demographic model of urbanization and stability behaviour of a social group by means of loop analysis, thermodynamic criteria of stability and stochastic criteria of stability. The book will be useful to the researchers and graduate students who wish to pursue research in mathematical ecology.

Stochastic Models in Biology

Stochastic Models in Biology

Author: Narendra S. Goel

Publisher: Elsevier

Published: 2013-10-22

Total Pages: 282

ISBN-13: 1483278107

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Stochastic Models in Biology describes the usefulness of the theory of stochastic process in studying biological phenomena. The book describes analysis of biological systems and experiments though probabilistic models rather than deterministic methods. The text reviews the mathematical analyses for modeling different biological systems such as the random processes continuous in time and discrete in state space. The book also discusses population growth and extinction through Malthus' law and the work of MacArthur and Wilson. The text then explains the dynamics of a population of interacting species. The book also addresses population genetics under systematic evolutionary pressures known as deterministic equations and genetic changes in a finite population known as stochastic equations. The text then turns to stochastic modeling of biological systems at the molecular level, particularly the kinetics of biochemical reactions. The book also presents various useful equations such as the differential equation for generating functions for birth and death processes. The text can prove valuable for biochemists, cellular biologists, and researchers in the medical and chemical field who are tasked to perform data analysis.


Book Synopsis Stochastic Models in Biology by : Narendra S. Goel

Download or read book Stochastic Models in Biology written by Narendra S. Goel and published by Elsevier. This book was released on 2013-10-22 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Models in Biology describes the usefulness of the theory of stochastic process in studying biological phenomena. The book describes analysis of biological systems and experiments though probabilistic models rather than deterministic methods. The text reviews the mathematical analyses for modeling different biological systems such as the random processes continuous in time and discrete in state space. The book also discusses population growth and extinction through Malthus' law and the work of MacArthur and Wilson. The text then explains the dynamics of a population of interacting species. The book also addresses population genetics under systematic evolutionary pressures known as deterministic equations and genetic changes in a finite population known as stochastic equations. The text then turns to stochastic modeling of biological systems at the molecular level, particularly the kinetics of biochemical reactions. The book also presents various useful equations such as the differential equation for generating functions for birth and death processes. The text can prove valuable for biochemists, cellular biologists, and researchers in the medical and chemical field who are tasked to perform data analysis.

Stochastic Models for Structured Populations

Stochastic Models for Structured Populations

Author: Sylvie Meleard

Publisher: Springer

Published: 2015-09-03

Total Pages: 111

ISBN-13: 3319217119

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In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France). Vincent Bansaye and Sylvie Méléard are Professors at Ecole Polytechnique (France). They are a specialists of branching processes and random particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution.


Book Synopsis Stochastic Models for Structured Populations by : Sylvie Meleard

Download or read book Stochastic Models for Structured Populations written by Sylvie Meleard and published by Springer. This book was released on 2015-09-03 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France). Vincent Bansaye and Sylvie Méléard are Professors at Ecole Polytechnique (France). They are a specialists of branching processes and random particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution.

Stochastic Modelling and Control

Stochastic Modelling and Control

Author: M. H. A. Davis

Publisher: Springer

Published: 1985

Total Pages: 416

ISBN-13:

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This book aims to provide a unified treatment of input/output modelling and of control for discrete-time dynamical systems subject to random disturbances. The results presented are of wide applica bility in control engineering, operations research, econometric modelling and many other areas. There are two distinct approaches to mathematical modelling of physical systems: a direct analysis of the physical mechanisms that comprise the process, or a 'black box' approach based on analysis of input/output data. The second approach is adopted here, although of course the properties ofthe models we study, which within the limits of linearity are very general, are also relevant to the behaviour of systems represented by such models, however they are arrived at. The type of system we are interested in is a discrete-time or sampled-data system where the relation between input and output is (at least approximately) linear and where additive random dis turbances are also present, so that the behaviour of the system must be investigated by statistical methods. After a preliminary chapter summarizing elements of probability and linear system theory, we introduce in Chapter 2 some general linear stochastic models, both in input/output and state-space form. Chapter 3 concerns filtering theory: estimation of the state of a dynamical system from noisy observations. As well as being an important topic in its own right, filtering theory provides the link, via the so-called innovations representation, between input/output models (as identified by data analysis) and state-space models, as required for much contemporary control theory.


Book Synopsis Stochastic Modelling and Control by : M. H. A. Davis

Download or read book Stochastic Modelling and Control written by M. H. A. Davis and published by Springer. This book was released on 1985 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide a unified treatment of input/output modelling and of control for discrete-time dynamical systems subject to random disturbances. The results presented are of wide applica bility in control engineering, operations research, econometric modelling and many other areas. There are two distinct approaches to mathematical modelling of physical systems: a direct analysis of the physical mechanisms that comprise the process, or a 'black box' approach based on analysis of input/output data. The second approach is adopted here, although of course the properties ofthe models we study, which within the limits of linearity are very general, are also relevant to the behaviour of systems represented by such models, however they are arrived at. The type of system we are interested in is a discrete-time or sampled-data system where the relation between input and output is (at least approximately) linear and where additive random dis turbances are also present, so that the behaviour of the system must be investigated by statistical methods. After a preliminary chapter summarizing elements of probability and linear system theory, we introduce in Chapter 2 some general linear stochastic models, both in input/output and state-space form. Chapter 3 concerns filtering theory: estimation of the state of a dynamical system from noisy observations. As well as being an important topic in its own right, filtering theory provides the link, via the so-called innovations representation, between input/output models (as identified by data analysis) and state-space models, as required for much contemporary control theory.

Evolution from a Thermodynamic Perspective

Evolution from a Thermodynamic Perspective

Author: Carl F Jordan

Publisher: Springer Nature

Published: 2021-11-26

Total Pages: 383

ISBN-13: 3030851869

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Survival of the fittest” is a tautology, because those that are “fit” are the ones that survive, but to survive, a species must be “fit”. Modern evolutionary theory avoids the problem by defining fitness as reproductive success, but the complexity of life that we see today could not have evolved based on selection that favors only reproductive ability. There is nothing inherent in reproductive success alone that could result in higher forms of life. Evolution from a Thermodynamic Perspective presents a non-circular definition of fitness and a thermodynamic definition of evolution. Fitness means maximization of power output, necessary to survive in a competitive world. Evolution is the “storage of entropy”. “Entropy storage” means that solar energy, instead of dissipating as heat in the Earth, is stored in the structure of living organisms and ecosystems. Part one explains this in terms comprehensible to a scientific audience beyond biophysicists and ecosystem modelers. Part two applies thermodynamic theory in non-esoteric language to sustainability of agriculture, and to conservation of endangered species. While natural systems are stabilized by feedback, agricultural systems remain in a mode of perpetual growth, pressured by balance of trade and by a swelling population. The constraints imposed by thermodynamic laws are being increasingly felt as economic expansion destabilizes resource systems on which expansion depends.


Book Synopsis Evolution from a Thermodynamic Perspective by : Carl F Jordan

Download or read book Evolution from a Thermodynamic Perspective written by Carl F Jordan and published by Springer Nature. This book was released on 2021-11-26 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Survival of the fittest” is a tautology, because those that are “fit” are the ones that survive, but to survive, a species must be “fit”. Modern evolutionary theory avoids the problem by defining fitness as reproductive success, but the complexity of life that we see today could not have evolved based on selection that favors only reproductive ability. There is nothing inherent in reproductive success alone that could result in higher forms of life. Evolution from a Thermodynamic Perspective presents a non-circular definition of fitness and a thermodynamic definition of evolution. Fitness means maximization of power output, necessary to survive in a competitive world. Evolution is the “storage of entropy”. “Entropy storage” means that solar energy, instead of dissipating as heat in the Earth, is stored in the structure of living organisms and ecosystems. Part one explains this in terms comprehensible to a scientific audience beyond biophysicists and ecosystem modelers. Part two applies thermodynamic theory in non-esoteric language to sustainability of agriculture, and to conservation of endangered species. While natural systems are stabilized by feedback, agricultural systems remain in a mode of perpetual growth, pressured by balance of trade and by a swelling population. The constraints imposed by thermodynamic laws are being increasingly felt as economic expansion destabilizes resource systems on which expansion depends.

Deterministic Mathematical Models in Population Ecology

Deterministic Mathematical Models in Population Ecology

Author: Herbert I. Freedman

Publisher:

Published: 1980

Total Pages: 280

ISBN-13:

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Single-species growth; Pedration and parasitism; Predador-prey systems; Lotka-volterra systems for predator-prey interactions; Intermediate predator-prey models; Continous models; Discrete models; The kolmogorov model; Related topics and applications; Related topics; Aplications; competition and cooperation (symbiosis); Lotka-volterra competition models; Higher-oder competition models; cooperation (symbiosis); Pertubation theory; The implicit function theorem; Existence and Uniqueness of solutions of ordinary differential equations; Stability and periodicity; The poincare-bendixon theorem; The hopf bifurcation theorem.


Book Synopsis Deterministic Mathematical Models in Population Ecology by : Herbert I. Freedman

Download or read book Deterministic Mathematical Models in Population Ecology written by Herbert I. Freedman and published by . This book was released on 1980 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Single-species growth; Pedration and parasitism; Predador-prey systems; Lotka-volterra systems for predator-prey interactions; Intermediate predator-prey models; Continous models; Discrete models; The kolmogorov model; Related topics and applications; Related topics; Aplications; competition and cooperation (symbiosis); Lotka-volterra competition models; Higher-oder competition models; cooperation (symbiosis); Pertubation theory; The implicit function theorem; Existence and Uniqueness of solutions of ordinary differential equations; Stability and periodicity; The poincare-bendixon theorem; The hopf bifurcation theorem.

Energy Research Abstracts

Energy Research Abstracts

Author:

Publisher:

Published: 1985

Total Pages: 716

ISBN-13:

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Book Synopsis Energy Research Abstracts by :

Download or read book Energy Research Abstracts written by and published by . This book was released on 1985 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Transport and Interactions of Chlorides in Cement-based Materials

Transport and Interactions of Chlorides in Cement-based Materials

Author: Caijun Shi

Publisher: CRC Press

Published: 2019-07-26

Total Pages: 250

ISBN-13: 0429881975

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Chloride-induced corrosion is the most important durability issue of reinforced concrete structures, and the prediction and prevention of chloride-induced corrosion has attracted considerable interest all over the world. Given that chloride penetrates through the concrete cover, the issues concerning its transport are crucial. These include testing methods, prediction, and the prevention of ingress. During the transport process, physical and chemical interaction occurs between chloride and cement hydrates, which in turn affects the further transport, so the transport of chloride and these interactions are closely related and underpin our understanding of chloride-induced corrosion in RC structures. This book provides in-depth discussion of chloride transport and its interaction in cement-based materials, and reviews and summarizes the state of the art. The mechanisms and testing methods for chloride transport, chemical interactions of chloride with cement hydrates, chloride binding isotherms, measurement of penetration depths, factors affecting chloride transport, and modeling of chloride transport are discussed in detail. This book serves as a reference for researchers or engineer, and a textbook for graduate students.


Book Synopsis Transport and Interactions of Chlorides in Cement-based Materials by : Caijun Shi

Download or read book Transport and Interactions of Chlorides in Cement-based Materials written by Caijun Shi and published by CRC Press. This book was released on 2019-07-26 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chloride-induced corrosion is the most important durability issue of reinforced concrete structures, and the prediction and prevention of chloride-induced corrosion has attracted considerable interest all over the world. Given that chloride penetrates through the concrete cover, the issues concerning its transport are crucial. These include testing methods, prediction, and the prevention of ingress. During the transport process, physical and chemical interaction occurs between chloride and cement hydrates, which in turn affects the further transport, so the transport of chloride and these interactions are closely related and underpin our understanding of chloride-induced corrosion in RC structures. This book provides in-depth discussion of chloride transport and its interaction in cement-based materials, and reviews and summarizes the state of the art. The mechanisms and testing methods for chloride transport, chemical interactions of chloride with cement hydrates, chloride binding isotherms, measurement of penetration depths, factors affecting chloride transport, and modeling of chloride transport are discussed in detail. This book serves as a reference for researchers or engineer, and a textbook for graduate students.

Non-Local Partial Differential Equations for Engineering and Biology

Non-Local Partial Differential Equations for Engineering and Biology

Author: Nikos I. Kavallaris

Publisher: Springer

Published: 2018-09-01

Total Pages: 0

ISBN-13: 9783319885155

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This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.


Book Synopsis Non-Local Partial Differential Equations for Engineering and Biology by : Nikos I. Kavallaris

Download or read book Non-Local Partial Differential Equations for Engineering and Biology written by Nikos I. Kavallaris and published by Springer. This book was released on 2018-09-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.

Stochastic Nonlinear Systems in Physics, Chemistry, and Biology

Stochastic Nonlinear Systems in Physics, Chemistry, and Biology

Author: L. Arnold

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 239

ISBN-13: 3642680380

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This book contains the invited papers of the interdisciplinary workshop on "Stochastic Nonlinear Systems in Physics, Chemistry and Biology" held at the Center for Interdisciplinary Research (ZIF), University of Bielefeld, West Germany, October 5-11, 1980. The workshop brought some 25 physicists, chemists, and biologists - who deal with stochastic phenomena - and about an equal number of mathematicians - who are experts in the theory of stochastic processes - together. The Scientific Commitee consisted of L. Arnold (Bremen), A. Dress (Bielefeld), W. Horsthemke (Brussels), T. Kurtz (Madison), R. Lefever (Brussels), G. Nicolis (Brussels), and V. Wihstutz (Bremen). The main topics of the workshop were the transition from deterministic to stoch astic behavior, external noise and noise induced transitions, internal fluctuations, phase transitions, and irreversible thermodynamics, and on the mathematical side, approximation of stochastic processes, qualitative theory of stochastic systems, and space-time processes. The workshop was sponsored by ZIF, Bielefeld, and by the Universities of Bremen and Brussels. We would like to thank the staff of ZIF and H. Crauel and M. Ehrhardt (Bremen) for the perfect organization and their assistance. In addition, our thanks go to Professor H. Haken for having these Proceedings included in the Se ries in Synergetics. Bremen and Brussels L. Arnold and R. Lefever December 1980 v Contents Part I. Introduction: From Deterministic to Stochastic Behavior On the Foundations of Kinetic Theory By B. Misr~ and I. Prigogine (With 1 Figure) ............................. .


Book Synopsis Stochastic Nonlinear Systems in Physics, Chemistry, and Biology by : L. Arnold

Download or read book Stochastic Nonlinear Systems in Physics, Chemistry, and Biology written by L. Arnold and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the invited papers of the interdisciplinary workshop on "Stochastic Nonlinear Systems in Physics, Chemistry and Biology" held at the Center for Interdisciplinary Research (ZIF), University of Bielefeld, West Germany, October 5-11, 1980. The workshop brought some 25 physicists, chemists, and biologists - who deal with stochastic phenomena - and about an equal number of mathematicians - who are experts in the theory of stochastic processes - together. The Scientific Commitee consisted of L. Arnold (Bremen), A. Dress (Bielefeld), W. Horsthemke (Brussels), T. Kurtz (Madison), R. Lefever (Brussels), G. Nicolis (Brussels), and V. Wihstutz (Bremen). The main topics of the workshop were the transition from deterministic to stoch astic behavior, external noise and noise induced transitions, internal fluctuations, phase transitions, and irreversible thermodynamics, and on the mathematical side, approximation of stochastic processes, qualitative theory of stochastic systems, and space-time processes. The workshop was sponsored by ZIF, Bielefeld, and by the Universities of Bremen and Brussels. We would like to thank the staff of ZIF and H. Crauel and M. Ehrhardt (Bremen) for the perfect organization and their assistance. In addition, our thanks go to Professor H. Haken for having these Proceedings included in the Se ries in Synergetics. Bremen and Brussels L. Arnold and R. Lefever December 1980 v Contents Part I. Introduction: From Deterministic to Stochastic Behavior On the Foundations of Kinetic Theory By B. Misr~ and I. Prigogine (With 1 Figure) ............................. .