nonlinear models of interacting populations

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On The Volterra And Other Nonlinear Models Of Interacting Populations Nonlinear Models In Interacting Populations

Author : N. S. Goel
ISBN : OCLC:959514051
Genre :
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Nonlinear Models Of Interacting Populations

Author : N Goel
ISBN : 9780323160933
Genre : Science
File Size : 56. 10 MB
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On the Volterra and Other Nonlinear Models of Interacting Populations explores the various models brought upon to investigate the different assemblies known to man. Assemblies include populations of various biological species, countries, and political parties among others. Because there are numerous assemblies to be measured and evaluated, it has been decided that a standard model be used to ascertain a detailed investigation. One of the models that have been brought forward is introduced by Volterra, which started as a basis for ecological processes. The book begins by establishing that Volterra’s model is one of the simplest nonlinear competition models. It explores the model through the study of the population growth of a species. It also covers other theories and concepts relating to the Volterra model in the context of the study. These include equilibrium theory, diversity and stability in ecological systems, and time lags in population among others. The book is a helpful reference for students, researchers, scientists, policymakers, and other parties in search of model/s that fully investigate different assemblies.

Nonlinear Dynamics Of Interacting Populations

Author : A. D. Bazykin
ISBN : 9810216858
Genre : Science
File Size : 61. 67 MB
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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.

On The Volterra And Other Nonlinear Models Of Interacting Populations By N S Geol S C Maitra And E W Montroll

Author : Narendra S. Goel
ISBN : OCLC:977436358
Genre : Animal populations
File Size : 52. 94 MB
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On The Volterra And Other Nonlinear Models Of Interacting Populations

Author : Narendra S. Goel
ISBN : UOM:39076006445907
Genre : Science
File Size : 56. 44 MB
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Modeling And Differential Equations In Biology

Author : T. A. Burton
ISBN : 9781351431026
Genre : Mathematics
File Size : 61. 20 MB
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First published in 1980. CRC Press is an imprint of Taylor & Francis.

Theory Of Nonlinear Age Dependent Population Dynamics

Author : Glenn F. Webb
ISBN : 0824772903
Genre : Mathematics
File Size : 56. 88 MB
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Mathematical Models In Biology

Author : Elizabeth S. Allman
ISBN : 0521525861
Genre : Mathematics
File Size : 47. 29 MB
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Linear and non-linear models of populations, molecular evolution, phylogenetic tree construction, genetics, and infectious diseases are presented with minimal prerequisites.

Concepts And Models Of A Quantitative Sociology

Author : W. Weidlich
ISBN : 9783642817892
Genre : Science
File Size : 22. 16 MB
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While the volumes hitherto published in the Springer Series in Synergetics have been devoted almost exclusively to the self-organized formation of structures in physics, chemistry and biology, the present monograph by Weidlich and Haag deals with the formation of "structures" (or "patterns") in society. At first glance it would seem a daring enterprise to deal with the complex processes in society using concepts and methods first developed in physics. But over the past decade it has been shown that there is a large class of phenomena in a variety of fields to which unifying concepts can be applied. This is particulary true of situations in which a system composed of many parts or individuals acquires a new structure on macroscopic scales. Indeed, this is the definition of synergetics which I formulated more than a decade ago, and which formed the basis of my survey on the profound analogies in the behaviour of complex systems, includ ing those of sociology (H. Haken: Synergetics. An Introduction, Volume 1 of this series). As I have pointed out on many occasions, the universal validity of these concepts is neither accidental nor is it caused by a mere extension of physical rules to other fields, but is instead a consequence of deep-rooted struc tural properties of systems of interacting parts which are due to rigorous mathe maticallaws. Generally speaking, concepts and methods originally used in physics can be applied to sociological phenomena in two ways.

Differential Equations Dynamical Systems And Linear Algebra

Author : Morris W. Hirsch
ISBN : 9780080873763
Genre : Mathematics
File Size : 74. 52 MB
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This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.

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