Stability of symmetric idiotypic networks-A critique of Hoffmann's analysis
Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter i...
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E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1989 |
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Elsevier Journal Backfiles on ScienceDirect 1907 - 2002 |
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| Übergeordnetes Werk: |
in: Bulletin of Mathematical Biology - Amsterdam : Elsevier, 51(1989), 2, Seite 217-222 |
| Übergeordnetes Werk: |
volume:51 ; year:1989 ; number:2 ; pages:217-222 |
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| 520 | |a Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis. | ||
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(DE-627)NLEJ185229018 (DE-599)GBVNLZ185229018 DE-627 ger DE-627 rakwb eng Stability of symmetric idiotypic networks-A critique of Hoffmann's analysis 1989 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis. Elsevier Journal Backfiles on ScienceDirect 1907 - 2002 De Boer, R.J. oth Hogeweg, P. oth in Bulletin of Mathematical Biology Amsterdam : Elsevier 51(1989), 2, Seite 217-222 (DE-627)NLEJ176866760 (DE-600)1462512-X 0092-8240 nnns volume:51 year:1989 number:2 pages:217-222 http://dx.doi.org/10.1016/S0092-8240(89)80069-2 GBV_USEFLAG_H ZDB-1-SDJ GBV_NL_ARTICLE AR 51 1989 2 217-222 |
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(DE-627)NLEJ185229018 (DE-599)GBVNLZ185229018 DE-627 ger DE-627 rakwb eng Stability of symmetric idiotypic networks-A critique of Hoffmann's analysis 1989 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis. Elsevier Journal Backfiles on ScienceDirect 1907 - 2002 De Boer, R.J. oth Hogeweg, P. oth in Bulletin of Mathematical Biology Amsterdam : Elsevier 51(1989), 2, Seite 217-222 (DE-627)NLEJ176866760 (DE-600)1462512-X 0092-8240 nnns volume:51 year:1989 number:2 pages:217-222 http://dx.doi.org/10.1016/S0092-8240(89)80069-2 GBV_USEFLAG_H ZDB-1-SDJ GBV_NL_ARTICLE AR 51 1989 2 217-222 |
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(DE-627)NLEJ185229018 (DE-599)GBVNLZ185229018 DE-627 ger DE-627 rakwb eng Stability of symmetric idiotypic networks-A critique of Hoffmann's analysis 1989 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis. Elsevier Journal Backfiles on ScienceDirect 1907 - 2002 De Boer, R.J. oth Hogeweg, P. oth in Bulletin of Mathematical Biology Amsterdam : Elsevier 51(1989), 2, Seite 217-222 (DE-627)NLEJ176866760 (DE-600)1462512-X 0092-8240 nnns volume:51 year:1989 number:2 pages:217-222 http://dx.doi.org/10.1016/S0092-8240(89)80069-2 GBV_USEFLAG_H ZDB-1-SDJ GBV_NL_ARTICLE AR 51 1989 2 217-222 |
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(DE-627)NLEJ185229018 (DE-599)GBVNLZ185229018 DE-627 ger DE-627 rakwb eng Stability of symmetric idiotypic networks-A critique of Hoffmann's analysis 1989 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis. Elsevier Journal Backfiles on ScienceDirect 1907 - 2002 De Boer, R.J. oth Hogeweg, P. oth in Bulletin of Mathematical Biology Amsterdam : Elsevier 51(1989), 2, Seite 217-222 (DE-627)NLEJ176866760 (DE-600)1462512-X 0092-8240 nnns volume:51 year:1989 number:2 pages:217-222 http://dx.doi.org/10.1016/S0092-8240(89)80069-2 GBV_USEFLAG_H ZDB-1-SDJ GBV_NL_ARTICLE AR 51 1989 2 217-222 |
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(DE-627)NLEJ185229018 (DE-599)GBVNLZ185229018 DE-627 ger DE-627 rakwb eng Stability of symmetric idiotypic networks-A critique of Hoffmann's analysis 1989 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis. Elsevier Journal Backfiles on ScienceDirect 1907 - 2002 De Boer, R.J. oth Hogeweg, P. oth in Bulletin of Mathematical Biology Amsterdam : Elsevier 51(1989), 2, Seite 217-222 (DE-627)NLEJ176866760 (DE-600)1462512-X 0092-8240 nnns volume:51 year:1989 number:2 pages:217-222 http://dx.doi.org/10.1016/S0092-8240(89)80069-2 GBV_USEFLAG_H ZDB-1-SDJ GBV_NL_ARTICLE AR 51 1989 2 217-222 |
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Stability of symmetric idiotypic networks-A critique of Hoffmann's analysis |
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Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis. |
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Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis. |
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Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis. |
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