# Dresden 2020 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 12: Statistical Physics of Biological Systems I (joint session BP/DY)

### DY 12.3: Vortrag

### Montag, 16. März 2020, 15:30–15:45, SCH A251

Kauffman NK models interpolated between K=2 and K=3 — James E. Sullivan, Dmitry Nerukh, and •Jens Christian Claussen — Department of Mathematics, Aston University, Birmingham B4 7ET, U.K.

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 K_{i} 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).