Structural And Dynamic Stability Of Model Predator Prey Systems

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Introduction to Functional Differential Equations

Author : Jack K. Hale
Publisher : Springer Science & Business Media
ISBN 13 : 1461243424
Total Pages : 458 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Introduction to Functional Differential Equations by : Jack K. Hale

Download or read book Introduction to Functional Differential Equations written by Jack K. Hale and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a complete new presentation of lin ear systems (Chapters 6~9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global at tractors was completely revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (see Chapters 1, 2, 3, 9, and 10). Chapter 12 is completely new and contains a guide to active topics of re search. In the sections on supplementary remarks, we have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive. Jack K. Hale Sjoerd M. Verduyn Lunel Contents Preface............................................................ v Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 1. Linear differential difference equations . . . . . . . . . . . . . . 11 . . . . . . 1.1 Differential and difference equations. . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . 1.2 Retarded differential difference equations. . . . . . . . . . . . . . . . 13 . . . . . . . 1.3 Exponential estimates of x( ¢,f) . . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . . . 1.4 The characteristic equation . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . 1.5 The fundamental solution. . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . 1.6 The variation-of-constants formula............................. 23 1. 7 Neutral differential difference equations . . . . . . . . . . . . . . . . . 25 . . . . . . . 1.8 Supplementary remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 34 . . . . . . . . . . . . . 2. Functional differential equations: Basic theory . . . . . . . . 38 . . 2.1 Definition of a retarded equation. . . . . . . . . . . . . . . . . . . . . . 38 . . . . . . . . . 2.2 Existence, uniqueness, and continuous dependence . . . . . . . . . . 39 . . . 2.3 Continuation of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 44 . . . . . . . . . . . .

Nonlinear Dynamics of Interacting Populations

Author : A. D. Bazykin
Publisher : World Scientific
ISBN 13 : 9789810216856
Total Pages : 224 pages
Book Rating : 4.2/5 (168 download)

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Book Synopsis Nonlinear Dynamics of Interacting Populations by : A. D. Bazykin

Download or read book Nonlinear Dynamics of Interacting Populations written by A. D. Bazykin and published by World Scientific. This book was released on 1998 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative theory of dynamical systems — most importantly bifurcation theory, which describes the dependence of a system on the parameters. This approach allows one to find general patterns of behavior that are expected to be observed in ecological models. Of special interest is the reaction of a given model to disturbances of its present state, as well as to changes in the external conditions. This leads to the general idea of “dangerous boundaries” in the state and parameter space of an ecological system. The study of these boundaries allows one to analyze and predict qualitative and often sudden changes of the dynamics — a much-needed tool, given the increasing antropogenic load on the biosphere.As a spin-off from this approach, the book can be used as a guided tour of bifurcation theory from the viewpoint of application. The interested reader will find a wealth of intriguing examples of how known bifurcations occur in applications. The book can in fact be seen as bridging the gap between mathematical biology and bifurcation theory.

Complex Population Dynamics

Author : Peter Turchin
Publisher : Princeton University Press
ISBN 13 : 0691090211
Total Pages : 470 pages
Book Rating : 4.6/5 (91 download)

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Book Synopsis Complex Population Dynamics by : Peter Turchin

Download or read book Complex Population Dynamics written by Peter Turchin and published by Princeton University Press. This book was released on 2003-02-02 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why do organisms become extremely abundant one year and then seem to disappear a few years later? Why do population outbreaks in particular species happen more or less regularly in certain locations, but only irregularly (or never at all) in other locations? Complex population dynamics have fascinated biologists for decades. By bringing together mathematical models, statistical analyses, and field experiments, this book offers a comprehensive new synthesis of the theory of population oscillations. Peter Turchin first reviews the conceptual tools that ecologists use to investigate population oscillations, introducing population modeling and the statistical analysis of time series data. He then provides an in-depth discussion of several case studies--including the larch budmoth, southern pine beetle, red grouse, voles and lemmings, snowshoe hare, and ungulates--to develop a new analysis of the mechanisms that drive population oscillations in nature. Through such work, the author argues, ecologists can develop general laws of population dynamics that will help turn ecology into a truly quantitative and predictive science. Complex Population Dynamics integrates theoretical and empirical studies into a major new synthesis of current knowledge about population dynamics. It is also a pioneering work that sets the course for ecology's future as a predictive science.

FWS/OBS.

Author :
Publisher :
ISBN 13 :
Total Pages : 644 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis FWS/OBS. by :

Download or read book FWS/OBS. written by and published by . This book was released on 1980 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt:

System Zoo 2 Simulation Models

Author : Hartmut Bossel
Publisher : BoD – Books on Demand
ISBN 13 : 3833484233
Total Pages : 206 pages
Book Rating : 4.8/5 (334 download)

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Book Synopsis System Zoo 2 Simulation Models by : Hartmut Bossel

Download or read book System Zoo 2 Simulation Models written by Hartmut Bossel and published by BoD – Books on Demand. This book was released on 2007 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling and computer simulation make it possible to understand and control the dynamic processes taking place in complex systems. Simulation provides insights into the often surprising diversity of possible behaviors, and allows identifying possibilities for intervention and options for alternative development. About one hundred simulation models from all areas of life are fully documented in the three volumes of the 'System Zoo'. They can be quickly implemented and easily operated using freely available system dynamics software. Volume 2 of the System Zoo contains simulation models of the regional water cycle and global carbon cycle, the photosynthesis of vegetation, forest growth, the water, nutrient, and energy dynamics of agriculture, the interaction of plants, animals, and humans with other organisms and resources by predation, harvesting, and competition for nutrients, and through utilization of renewable and exploitation of nonrenewable resources. The System Zoo collection of simulation models is particularly well-suited for teaching, training, and research projects at all levels from high school to university, and for individual study. Volume 1 of the System Zoo contains simulation models of elementary systems, and of systems from the fields of physics and engineering. Volume 3 deals with systems and processes found in economy and society, and with long-term global development. Hartmut Bossel is Professor Emeritus of environmental systems analysis. He taught for many years at the University of California in Santa Barbara and the University of Kassel, Germany, where he was director of the Center for Environmental Systems Research until his retirement. He holds an engineering degree from the Technical University of Darmstadt, and a Ph.D. degree from the University of California at Berkeley. With a background in engineering, systems science, and mathematical modeling, he has led many research projects and future studies in different countries, developing computer simulation models and decision support systems in the areas of energy supply policy, global dynamics, orientation of behavior, agricultural policy, and forest dynamics and management. He has written numerous books on modeling and simulation of dynamic systems, social change and future paths, and has published widely in the scientific literature in several fields.

Foundations of Ecological Resilience

Author : Lance H. Gunderson
Publisher : Island Press
ISBN 13 : 1610911334
Total Pages : 497 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Foundations of Ecological Resilience by : Lance H. Gunderson

Download or read book Foundations of Ecological Resilience written by Lance H. Gunderson and published by Island Press. This book was released on 2012-07-16 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ecological resilience provides a theoretical foundation for understanding how complex systems adapt to and recover from localized disturbances like hurricanes, fires, pest outbreaks, and floods, as well as large-scale perturbations such as climate change. Ecologists have developed resilience theory over the past three decades in an effort to explain surprising and nonlinear dynamics of complex adaptive systems. Resilience theory is especially important to environmental scientists for its role in underpinning adaptive management approaches to ecosystem and resource management. Foundations of Ecological Resilience is a collection of the most important articles on the subject of ecological resilience—those writings that have defined and developed basic concepts in the field and help explain its importance and meaning for scientists and researchers. The book’s three sections cover articles that have shaped or defined the concepts and theories of resilience, including key papers that broke new conceptual ground and contributed novel ideas to the field; examples that demonstrate ecological resilience in a range of ecosystems; and articles that present practical methods for understanding and managing nonlinear ecosystem dynamics. Foundations of Ecological Resilience is an important contribution to our collective understanding of resilience and an invaluable resource for students and scholars in ecology, wildlife ecology, conservation biology, sustainability, environmental science, public policy, and related fields.

Biological Evaluation of Environmental Impacts

Author :
Publisher :
ISBN 13 :
Total Pages : 380 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Biological Evaluation of Environmental Impacts by :

Download or read book Biological Evaluation of Environmental Impacts written by and published by . This book was released on 1980 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Predator-prey Systems in Fisheries Management

Author : Henry Clepper
Publisher :
ISBN 13 :
Total Pages : 522 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Predator-prey Systems in Fisheries Management by : Henry Clepper

Download or read book Predator-prey Systems in Fisheries Management written by Henry Clepper and published by . This book was released on 1979 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Structured Population Dynamics

Author : J. M. Cushing
Publisher : SIAM
ISBN 13 : 9781611970005
Total Pages : 106 pages
Book Rating : 4.9/5 (7 download)

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Book Synopsis An Introduction to Structured Population Dynamics by : J. M. Cushing

Download or read book An Introduction to Structured Population Dynamics written by J. M. Cushing and published by SIAM. This book was released on 1998-01-01 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in the temporal fluctuations of biological populations can be traced to the dawn of civilization. How can mathematics be used to gain an understanding of population dynamics? This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models. This theory bridges the gap between the characteristics of individual organisms in a population and the dynamics of the total population as a whole. In this monograph, many applications that illustrate both the theory and a wide variety of biological issues are given, along with an interdisciplinary case study that illustrates the connection of models with the data and the experimental documentation of model predictions. The author also discusses the use of discrete and continuous models and presents a general modeling theory for structured population dynamics. Cushing begins with an obvious point: individuals in biological populations differ with regard to their physical and behavioral characteristics and therefore in the way they interact with their environment. Studying this point effectively requires the use of structured models. Specific examples cited throughout support the valuable use of structured models. Included among these are important applications chosen to illustrate both the mathematical theories and biological problems that have received attention in recent literature.

Optimal Control Applied to Biological Models

Author : Suzanne Lenhart
Publisher : CRC Press
ISBN 13 : 1420011413
Total Pages : 272 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Optimal Control Applied to Biological Models by : Suzanne Lenhart

Download or read book Optimal Control Applied to Biological Models written by Suzanne Lenhart and published by CRC Press. This book was released on 2007-05-07 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into t

Justified Modeling Frameworks and Novel Interpretations of Ecological and Epidemiological Systems

Author : Bapan Ghosh
Publisher : Frontiers Media SA
ISBN 13 : 2832540147
Total Pages : 151 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Justified Modeling Frameworks and Novel Interpretations of Ecological and Epidemiological Systems by : Bapan Ghosh

Download or read book Justified Modeling Frameworks and Novel Interpretations of Ecological and Epidemiological Systems written by Bapan Ghosh and published by Frontiers Media SA. This book was released on 2024-01-12 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Lotka-Volterra and the Kermack-McKendrick models are well celebrated and widely recognized in the field of ecology and epidemiology. Several modified ordinary differential equation models have been proposed over the last many decades to rationalize complex biological phenomena. In the current century, researchers have paid much attention to developing new modeling frameworks with delay differential equations, difference equations, fractional order systems, stochastic differential equations, etc. No doubt, these models have emerged many new bifurcations theory and methods which have equally contributed to the advances of Mathematics and interdisciplinary research. It is argued that these new modeling frameworks perform more effectively in analyzing and interpreting results compared to the conventional modeling frameworks with ordinary differential equations. However, implications of emerged bifurcations from new modeling approaches are often less interpreted from a biological viewpoint. Even, there is also a lack of understanding of how a fractional order model, for instance, displays a more realistic scenario to analyze a biological process. Therefore, a more serious justification is essential while modeling any biological event.

Synesthesia Decodes Innovation: The Dante Effect

Author : Dingping (Frank) Qian
Publisher : World Scientific
ISBN 13 : 9811249709
Total Pages : 525 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Synesthesia Decodes Innovation: The Dante Effect by : Dingping (Frank) Qian

Download or read book Synesthesia Decodes Innovation: The Dante Effect written by Dingping (Frank) Qian and published by World Scientific. This book was released on 2024-05-28 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the Collaboration of Cotter LiThe process of decrypting innovation and creation, as a lurking nondescript so far, is theorized and operationalized based upon interdisciplinary taskings.First comes the mapping between real world and human brain; innovation is redefined as discovering new interrelationships in the brain using an algorithm, well-defined in 5 steps, of searching unknown relations herein, and the psychological synesthesia governing communications in the brain is dutifully augmented and made to function accordingly. The Dante effect then binds the fresh interactions into a metaphoric tome which is mapped back to the real world to become an up-to-date theory or a new appliance.Since the author has been nurtured both in Chinese spiritual excellence and advanced Western cultures, this book is penned in a provocative style of knowledgeably poetic prose that will appeal to a broad audience.In the era of Artificial Intelligence, it is the human capacity of Thinking Synesthesia acquitted itself with distinction in the profound understanding of various interrelationships that transcends time and will be blessed with eternal youth.

Fractional Derivatives with Mittag-Leffler Kernel

Author : José Francisco Gómez
Publisher : Springer
ISBN 13 : 303011662X
Total Pages : 339 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Fractional Derivatives with Mittag-Leffler Kernel by : José Francisco Gómez

Download or read book Fractional Derivatives with Mittag-Leffler Kernel written by José Francisco Gómez and published by Springer. This book was released on 2019-02-13 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks together with applications in different fields of science and engineering, such as chemistry, mechanics, epidemiology and more. It is intended as a timely guide and source of inspiration for graduate students and researchers in the above-mentioned areas.

Elements of Mathematical Ecology

Author : Mark Kot
Publisher : Cambridge University Press
ISBN 13 : 1316584054
Total Pages : 466 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Elements of Mathematical Ecology by : Mark Kot

Download or read book Elements of Mathematical Ecology written by Mark Kot and published by Cambridge University Press. This book was released on 2001-07-19 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems thoughout the text that aid understanding, and supplementary mathematical and historical material that enrich the main text.

Competition Theory in Ecology

Author : Peter A. Abrams
Publisher : Oxford University Press
ISBN 13 : 0192648098
Total Pages : 336 pages
Book Rating : 4.1/5 (926 download)

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Book Synopsis Competition Theory in Ecology by : Peter A. Abrams

Download or read book Competition Theory in Ecology written by Peter A. Abrams and published by Oxford University Press. This book was released on 2022-08-25 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Competition between species arises when two or more species share at least some of the same limited resources. It is likely to affect all species, as well as many higher-level aspects of community and ecosystem dynamics. Interspecific competition shares many of the same features as density dependence (intraspecific competition) and evolution (competition between genotypes). In spite of this, a robust theoretical framework is not yet in place to develop a more coherent understanding of this important interaction. Despite its prominence in the ecological literature, the theory seems to have lost direction in recent decades, with many synthetic papers promoting outdated ideas, failing to use resource-based models, and having little utility in applied fields such as conservation and environmental management. Competition theory has done little to incorporate new findings regarding consumer-resource interactions in the context of larger food webs containing behaviourally or evolutionarily adapting components. Overly simple models and methods of analysis continue to be influential. Competition Theory in Ecology represents a timely opportunity to address these shortcomings and suggests a more useful approach to modelling that can provide a basis for future models that have greater predictive ability in both ecology and evolution. The book concludes with some broader observations on the lack of agreement on general principles to use in constructing mathematical models to help understand ecological systems. It argues that a more open discussion and debate of the underlying structure of ecological theory is now urgently required to move the field forward.

Nonlinear Differential Equations and Dynamical Systems

Author : Feliz Manuel Minhós
Publisher : MDPI
ISBN 13 : 3036507108
Total Pages : 158 pages
Book Rating : 4.0/5 (365 download)

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Book Synopsis Nonlinear Differential Equations and Dynamical Systems by : Feliz Manuel Minhós

Download or read book Nonlinear Differential Equations and Dynamical Systems written by Feliz Manuel Minhós and published by MDPI. This book was released on 2021-04-15 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Mathematical Models in Population Biology and Epidemiology

Author : Fred Brauer
Publisher : Springer Science & Business Media
ISBN 13 : 1475735162
Total Pages : 432 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Mathematical Models in Population Biology and Epidemiology by : Fred Brauer

Download or read book Mathematical Models in Population Biology and Epidemiology written by Fred Brauer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.