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Nichtlineare Dynamik der Hypothesenbildung

Autor(en): N. Fürstenau
Zusammenfassung: The algebraic belief-adjustment model of Hogarth and Einhorn is used as a starting point for a nonlinear dynamical systems approach to decision making within the framework of Haken's Synergetics as theory of self-organization of complex systems. An equivalence is derived between the recursive belief-adjust-ment model and processes modeled by the Logistic equation with a single control parameter [Lambda]. It yields 1 <= [Lambda] <= 2 under Hogarths assumptions. It follows that for a sufficiently large number of belief updates the belief in a hypothesis in Hogarth's model always approaches a fixed point. Comparison with the Cohen-Grossberg dynamics suggests the interpretation of [Lambda] as gain parameter allowing for [Lambda] > 2. An increase of the control parameter to [Lambda] > 3 yields the well known universal period doubling bifurcations at critical values ?©n and deterministic chaos within 3.57 <= [Lambda]n <= 4. The transition from quadratic to cosinuidal maps yields node type bifurcations, which have been experimentally realized by photonic, interferomet-ric equivalent circuits. In agreement with the catastrophe theoretical approach to decision making they exhibit discontinuous transitions between different station-ary levels including hysteresis effects. In terms of Synergetics this process corresponds to the spontaneous symmetry breaking of a (belief-) potential energy function. It determines the belief state as a macroscopic order parameter which is driven by a conservative force as derivative of the potential. The example of bistable switching of the visual perception with ambiguous pictures reveals the relationship to the Synergetic theory of pattern recognition.
Veranstaltung: 44. Fachausschusssitzung Anthropotechnik der Deutschen Gesellschaft für Luft- und Raumfahrt - Lilienthal-Oberth e.V.;Langen
Medientyp: Conference Paper
Sprache: englisch
Veröffentlicht: DGLR-Bericht, 2002, 2002-04, Situation Awareness in der Fahrzeug- und Prozessführung; S.199-216; 2002; Deutsche Gesellschaft für Luft- und Raumfahrt - Lilienthal-Oberth e.V., Bonn
Preis: NA
Stichworte zum Inhalt: antropotechnik
Verfügbarkeit: Bestellbar
Veröffentlicht: 2002

Dieses Dokument ist Teil einer übergeordneten Publikation:
Situation Awareness in der Fahrzeug- und Prozessführung