Emergence and growth of complex networks in adaptive systems

Jain, Shaili; Krishna, S.

doi:10.1016/s0010-4655(99)00293-3

Cited by 32 publications

(27 citation statements)

References 7 publications

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“…We denote 1 (C) ϵ 1 . It can be shown (16) that if the graph does not have an ACS, then 1 ϭ 0, and if it does, then 1 Ն 1.…”

Section: Definitions and Notationmentioning

confidence: 99%

“…Dominant ACS. It can be shown that if 1 Ն 1 the subgraph comprising the populated species (X i Ͼ 0) must be an ACS (11,16), which will be referred to as the dominant ACS. The dominant ACS is uniquely determined by the graph and does not depend on the initial condition for x (except for special initial conditions forming a set of measure zero, which we ignore).…”

Section: Definitions and Notationmentioning

confidence: 99%

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Large extinctions in an evolutionary model: The role of innovation and keystone species

Jain

Krishna

2002

Proc. Natl. Acad. Sci. U.S.A.

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The causes of major and rapid transitions observed in biological macroevolution as well as in the evolution of social systems are a subject of much debate. Here we identify the proximate causes of crashes and recoveries that arise dynamically in a model system in which populations of (molecular) species coevolve with their network of chemical interactions. Crashes are events that involve the rapid extinction of many species, and recoveries the assimilation of new ones. These are analyzed and classified in terms of the structural properties of the network. We find that in the absence of large external perturbation, ''innovation'' is a major cause of large extinctions and the prime cause of recoveries. Another major cause of crashes is the extinction of a ''keystone species.'' Different classes of causes produce crashes of different characteristic sizes.

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“…We denote 1 (C) ϵ 1 . It can be shown (16) that if the graph does not have an ACS, then 1 ϭ 0, and if it does, then 1 Ն 1.…”

Section: Definitions and Notationmentioning

confidence: 99%

Section: Definitions and Notationmentioning

confidence: 99%

Large extinctions in an evolutionary model: The role of innovation and keystone species

Jain

Krishna

2002

Proc. Natl. Acad. Sci. U.S.A.

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“…(see [5,16] Further, Tahir et al [15] introduced fuzziness into an autocatalytic set. The definition for fuzzy autocatalytic set is given as below: Definition 9.…”

Section: Fuzzy Autocatalytic Setmentioning

confidence: 99%

On Fuzzy Autocatalytic Set

Ashaari

Ahmad²

2016

Int. J. of Pure and Appl. Math.

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Fuzzy autocatalytic set (FACS) is one of the branch from graph theory. This FACS is used to introduce the fuzziness on connectivity of a graph. The introduction of FACS has given more accurate concept in application according a real-life problem. In this paper, some properties on fuzzy autocatalytic set of a graph theory is presented. This result give a new insight of FACS which is then expand the development of Fuzzy autocatalytic set (FACS) in the future.

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“…The initial graph is chosen such that for all i j a t ij ϭ 1 with probability q and a t ij ϭ 0 with probability 1 Ϫ q. This model has been introduced in Jain and Krishna [17], based on the well-documented Bak-Sneppen model of evolution [11], and its properties have extensively been investigated in the literature [12][13][14][15][16], besides others.…”

Section: The Modelmentioning

confidence: 99%

Predicting crashes in a model of evolving networks

Krause

2004

Complexity

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We consider an evolving network of interacting species which exhibits self-organization. The system is characterized by repeated crashes in which a large number of species are extinct and subsequent recoveries. We investigate the macroscopic properties of this system before such crashes, concentrating on the variance of the relative population sizes of species and its evolution over time. A simple score function is constructed to determine the probability of a crash within a certain time interval to be used as a predictor for crashes. © 2004 Wiley Periodicals, Inc. Complexity 9: 24 -30, 2004 Key Words: crash; prediction; self-organization; evolving networks M any time series are characterized by rare but repeated large and sudden changes (crashes) with subsequent slow reversals (recoveries). Examples of such behavior include earthquakes, sand piles, the extinction of species in biological evolution, and chemical processes as well as social systems, where stock markets have been of particular interest. Empirical as well as theoretical contributions in most cases focus on the distribution of the size of such crashes and the waiting time between them. However, for practical applications it would be of great importance to find properties of these systems that allow to predict the occurrence of crashes. Recently it has been proposed that earthquakes are preceded by log-periodic oscillations [1,2]. A similar result has been reported for crashes in stock markets [3], and the literature mentioned therein, but the empirical evidence for these precursors in stock market crashes is thus far not conclusive. Furthermore, the origin of these oscillations remains undetected such that these precursors up to now lack a sound theoretical foundation for the mechanism causing the crash.In this article we consider a model of evolving networks of interacting species as has been found to be useful for a wide range of applications, e.g., in social systems [4 -6], evolutionary models [7,8], or chemical processes [9]. Investigating the network structure of such a model [10], finds that large crashes are the consequence of a structural change in the network itself, called a core-shift. A further result is that the network structure also affects the robustness of the network to minor exogenous changes causing crashes. In deriving these results it was necessary to know the complete structure of the network at any point of time; this we will call the microscopic properties of a network.

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Emergence and growth of complex networks in adaptive systems

Cited by 32 publications

References 7 publications

Large extinctions in an evolutionary model: The role of innovation and keystone species

Large extinctions in an evolutionary model: The role of innovation and keystone species

On Fuzzy Autocatalytic Set

Predicting crashes in a model of evolving networks

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