Connective stability of complex ecosystems.
TLDR
It is confirmed by May2 in a study of large systems in the ecological context that probability of stability generally decreases with the increase of the degree of connectedness among the parts of the system.Abstract:
IN 1970, Garner and Ashby1 asked an important question: “If a large system is assembled (connected) at random, or has grown haphazardly, should we expect it to be stable or unstable?” They snowed on a linear model that probability of stability generally decreases with the increase of the degree of connectedness among the parts of the system. This fact was confirmed by May2 in a study of large systems in the ecological context.read more
Citations
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Journal ArticleDOI
The complexity and stability of ecosystems
TL;DR: Early studies suggested that simple ecosystems were less stable than complex ones, but later studies came to the opposite conclusion as discussed by the authors. Confusion arose because of the many different meanings of "complexity" and "stability".
Journal ArticleDOI
Babel, or the ecological stability discussions: an inventory and analysis of terminology and a guide for avoiding confusion.
Volker Grimm,Christian Wissel +1 more
TL;DR: A strategy is derived that can help to dispel the existing ”confusion of tongues” on the subject of ”stability” and prevent its future recurrence, and consists of three questions that should be kept in mind when communicating about stability properties.
Babel, or the ecological stability discussions: an inventory and analysis
Volker Grimm,Christian Wissel +1 more
TL;DR: In this article, the authors present an inventory and analysis of dis-cussions of ecological stability, considering 163 defini- tions of 70 different stability concepts, and propose a strategy that can help to dispel the existing "confu- sion of tongues" on the subject of "stability" and prevent its future recurrence.
Journal ArticleDOI
Qualitative theory of compartmental systems
John A. Jacquez,Carl P. Simon +1 more
TL;DR: The authors complete the solution of a problem posed by Bellman and show that closed nonlinear, autonomous, n-compartment systems can show the full gamut of possible behaviors of systems of ODES.
Journal ArticleDOI
Effect of complexity on marine ecosystem models
TL;DR: The main recommendation is that the use of a single 'ultimate' ecosystem model is ill-advised, while the comparative and con- firmatory use of multiple 'minimum-realistic' models is strongly recommended.
References
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Journal ArticleDOI
Will a large complex system be stable
Robert M. May,Robert M. May +1 more
TL;DR: It is suggested that large complex systems which are assembled (connected) at random may be expected to be stable up to a certain critical level of connectance, and then, as this increases, to suddenly become unstable.
Book
General competitive analysis
Kenneth J. Arrow,Frank Hahn +1 more
TL;DR: General competitive analysis, General competitive analysis as mentioned in this paper, General Competitive Analysis (GCA), general competitive analysis (GCA), GCA, GCA(GCA), GCA
Book
Differential and Integral Inequalities
TL;DR: In this article, the author's mono graph "Differential- und integral-un gleichungen," with the subtitle "und ihre Anwendung bei Abschatzungs und Eindeutigkeitsproblemen" was published.
Journal ArticleDOI
Connectance of large dynamic (cybernetic) systems: critical values for stability.
TL;DR: The work described here was intended to add to present theoretical knowledge of stability in large systems, for instability usually appears as a self-generating catastrophe.