Berlin 2018 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 24: Complex Systems

DY 24.2: Vortrag

Dienstag, 13. März 2018, 10:15–10:30, BH-N 128

Analyzing the bifurcation behavior of complex systems via stochastic continuation - application to the Ising model — •Clemens Willers¹, Uwe Thiele¹, David Lloyd², Andrew Archer³, and Oliver Kamps¹ — ¹Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany — ²Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK — ³Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK

For many complex systems an analytical description of the macroscopic dynamics is not available, for instance, for systems that are described on the microscopic level by lattice- or agent-based models. These are frequently used in all natural sciences, social science, and economics. To analyse in this case the solution and bifurcation structure of the model on the level of macroscopic observables, one has to rely on equation free methods like stochastic continuation [1,2]. The question arising in this context is which kind of bifurcation diagrams can be extracted and how they relate to such diagrams of related mean-field models if available. Our contribution briefly introduces the method of stochastic continuation. As an example, we then investigate the bifurcation diagram of the two-dimensional Ising model without and with external field both, with stochastic continuation and in the corresponding mean field model. This includes a discussion of the scaling of the extracted solutions and its relation to the known critical exponents.

[1] S.A. Thomas et. al., Physica A, 464 (2016) 27-53 [2] D. Barkley et. al., SIAM J. Appl. Dyn. Syst. 5 (2006) 403-434