nonlinear models of interacting populations

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Nonlinear Models Of Interacting Populations

Author : N Goel
ISBN : 9780323160933
Genre : Science
File Size : 72. 83 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.

On The Volterra And Other Nonlinear Models Of Interacting Populations

Author : Narendra S. Goel
ISBN : UOM:39076006445907
Genre : Science
File Size : 52. 89 MB
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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 :
File Size : 37. 10 MB
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Nonlinear Dynamics Of Interacting Populations

Author : A. D. Bazykin
ISBN : 9810216858
Genre : Science
File Size : 57. 76 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.

Population Biology

Author : H.I. Freedman
ISBN : 9783642878930
Genre : Mathematics
File Size : 46. 89 MB
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This volume contains the Proceedings of the International Conference in Population Biology held at The University of Alberta, Edmonton, Canada from June 22 to June 30, 1982. The Conference was sponsored by The University of Alberta and The Canadian Applied Mathematics Society, and overlapped with the summer meeting of CAMS. The main objectives of this Conference were: to bring mathematicians and biologists together so that they may interact for their mutual benefit; to bring those researchers interested in modelling in ecology and those interested in modelling in genetics together; to bring in keynote speakers in the delineated areas; to have sessions of contributed papers; and to present the opportunity for researchers to conduct workshops. With the exception of the last one, the objec tives were carried out. In order to lend some focus to the Conference, the following themes were adopted: models of species growth, predator-prey, competition, mutualism, food webs, dispersion, age structure, stability, evolution of ecological parameters, evolution of behaviour, life history strategies, group and social selection, and evolution of genetic systems. There were speakers (invited and/or contributed papers) in each of these areas. Talks were given on Tuesday, June 22 to Friday, June 25 and on Monday, June 28 to Wednesday, June 30. On each day there were several talks by the principal speakers as well as contributed sessions. Altogether, there were ninety one papers given, of which twelve were by the principal speakers. There were one hundred and twenty-three registered participants from twelve different countries.

Theory Of Nonlinear Age Dependent Population Dynamics

Author : Glenn F. Webb
ISBN : 0824772903
Genre : Mathematics
File Size : 22. 74 MB
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Mathematical Models In Biology

Author : Elizabeth S. Allman
ISBN : 0521525861
Genre : Mathematics
File Size : 47. 18 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.

Modeling And Differential Equations In Biology

Author : T. A. Burton
ISBN : 9781351431026
Genre : Mathematics
File Size : 70. 27 MB
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First published in 1980. CRC Press is an imprint of Taylor & Francis.

Differential Equations Dynamical Systems And Linear Algebra

Author : Morris W. Hirsch
ISBN : 9780080873763
Genre : Mathematics
File Size : 44. 31 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.

Exactly Solvable Models Of Biological Invasion

Author : Sergei V. Petrovskii
ISBN : 1584885211
Genre : Mathematics
File Size : 25. 48 MB
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Much of our current knowledge on biological invasion was derived from field studies, but many recent advances relied heavily on mathematics and computing, particularly mathematical modeling. While numerical simulations are clearly a useful approach, they have some serious drawbacks. Approximations errors and the number of parameter values can have a significant impact on the simulation results, the extent of which often remains obscure. Such difficulties do not arise, however, when the problem can be solved analytically. Exactly Solvable Models of Biological Invasion demonstrates the advantages and methods of obtaining exact solutions of partial differential equations that describe nonlinear problems encountered in the study of invasive species spread. With emphasis on PDEs of diffusion-reaction type, the authors present a comprehensive collection of exactly solvable models and a unified, self-contained description of the relevant mathematical methods. In doing so, they also provide new insight into important issues such as the impact of the Allee effect, the impact of predation, and the interplay between different modes of species dispersal. Full calculation details make this presentation accessible to biologists as well as applied mathematicians, and a range of ecological examples and applications demonstrate the utility of exact methods in practice. Exact solutions provide an immediate, complete description of system dynamics for a wide class of initial conditions and serve as a convenient tool for testing numerical algorithms and codes used in more specialized studies. This book lays the groundwork for bringing the power of exactly solvable models to bear on real-world ecological problems.

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