An analysis of models describing predator‐prey interaction
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In this article, the existence of limit cycle oscillations in a model in which predator growth rate is a function of the concentration of prey has been investigated using the singular points and phase plane portraits of early predator-prey models.Abstract:
Mathematical models of the interaction between predator and host populations have been expressed as systems of nonlinear ordinary differential equations. Solutions of such systems may be periodic or aperiodic. Periodic, oscillatory solutions may depend on the initial conditions of the system or may be limit cycles. Aperiodic solutions can, but do not necessarily, exhibit oscillatory behavior. Therefore, it is important to characterize predatory-prey models on the basis of the possible types of solutions they may possess. This characterization can be accomplished using some well-known methods of nonlinear analysis. Examination of the system singular points and inspection of phase plane portraits have proved to be useful techniques for evaluating the effect of various modifications of early predator-prey models. Of particular interest is the existence of limit cycle oscillations in a model in which predator growth rate is a function of the concentration of prey.read more
Citations
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Stability of Grazing Systems: An Application of Predator-Prey Graphs
TL;DR: A considerable body of theory has been developed to deal with systems of populations at two or more trophic levels, or 'exploitation' systems, and much of the theory was developed with explicit or implicit reference to two animal populations, but herbivore ('predator')-plant ('prey') interaction is sufficiently similar in its general features to make the same approach useful.
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Resources: A Graphical-Mechanistic Approach to Competition and Predation
TL;DR: A graphical, equilibrium theory of resource competition allows prediction of the outcome of interactions between several consumers for the various classes of resources.
Journal ArticleDOI
The kinetics of functional response
TL;DR: Holling's Type II functional-response relationship is presented, and the formulations expressing the underlying organismal interactions which might generate such a relation arc generalized into the Type III response typical of predators showing learning behavior.
Journal ArticleDOI
The stability and the intrinsic growth rates of prey and predator populations
TL;DR: Intrinsic population growth rates calculated for eight species of prey and of their important predators showed that the prey had higher rates than their predators in two cases, in both of which the prey species are known to be self—limited.
Journal ArticleDOI
The Relationship between Coercion and Protest An Empirical Evaluation in Three Coercive States
TL;DR: In this article, two forms of the predator-prey model were used to test competing hypotheses for the relationship between coercion and protest, and the results showed stable, damped relationships in all three cases.
References
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Book
The struggle for existence
TL;DR: For three-quarters of a century past more has been written about natural selection and the struggle for existence that underlies the selective process, than perhaps about any other single idea in the whole realm of Biology as discussed by the authors.
Journal ArticleDOI
The Continuous Culture of Bacteria; a Theoretical and Experimental Study
TL;DR: It is concluded that continuous culture may usually be expected to show a five to tenfold increase in output as compared with a batch process.
Book
Growth and regulation of animal populations
TL;DR: Books, as a source that may involve the facts, opinion, literature, religion, and many others are the great friends to join with.
Journal ArticleDOI
Studies on the Growth and Feeding of Tetrahymena pyriformis in Axenic and Monoxenic Culture
C. R. Curds,A. Cockburn +1 more
TL;DR: There was evidence which suggested that the individual feeding rate of a ciliate was governed by the concentration of ciliates as well as the concentrations of bacteria present, and a model for ciliate feeding was derived.