BPCPPDYSOE21 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 12: Posters DY - Fluid Physics, Active Matter, Complex Fluids, Soft Matter and Glasses (joint session DY/BP)
DY 12.23: Poster
Montag, 22. März 2021, 14:00–16:30, DYp
Kauffman NK models interpolated between K=2 and K=3 — •James Sullivan, Dmitry Nerukh, and Jens Christian Claussen — Department of Mathematics, Aston University, Birmingham, UK
The NK model was introduced by Stuart Kauffman and coworkers [1] as a model for fitness landscapes with tunable ruggedness, to understand epistasis and pleiotropy in evolutionary biology. In the original formulation, fitness is defined as a sum of fitness functions for each locus, each depending on the locus itself and K other loci. Varying K from K=0 to K=N−1 leads to different ruggedness of the landscape. In previous work we introduced a generalization that allows to interpolate between integer values of K by allowing Ki to assume different values for each locus. We focus on the interpolation between the most widely studied cases of K=2 and K=3 and characterize the landscapes by study of their local minima. Here we transfer this approach to Random Boolean Networks and investigate attractor basins and limit cycles where the average K assumes integer and noninteger values. Relaxing the assumption of degree-homogeneity is an important step towards more realistic boolean network models, relevant to a broad range of applications in the dynamics of social systems and in systems biology.
[1] Kauffman, S.; Levin, S., Journal of Theoretical Biology. 128, 11 (1987); Kauffman, S.; Weinberger, E., Journal of Theoretical Biology. 141, 211 (1989).