UBC Faculty Research and Publications

Soliton Kinetic Equations with Non-Kolmogorovian Structure : A New Tool for Biological Modeling? Aerts, Diederik; Czachor, Marek; Gabora, Liane; Polk, Philippe


Non-commutative diagrams, where X → Y → Z is allowed and X → Z → Y is not, may equally well apply to Malusian experiments with photons traversing polarizers, and to sequences of elementary chemical reactions. This is why non-commutative probabilistic, logical, and dynamical structures necessarily occur in chemical or biological dynamics. We discuss several explicit examples of such systems and propose an exactly solvable nonlinear toy model of a “brain–heart” system. The model involves non-Kolmogorovian probability calculus and soliton kinetic equations integrable by Darboux transformations.

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