TY - JOUR
T1 - Mesoscale symmetries explain dynamical equivalence of food webs
AU - Aufderheide, Helge E
AU - Rudolf, Lars
AU - Gross, Thilo
PY - 2012
Y1 - 2012
N2 - A present challenge in complex systems is to identify mesoscale structures that have distinct dynamical implications. In this paper we present a detailed investigation of a previously observed dynamical equivalence of certian ecological food webs. We show that this equivalence is rooted in mesoscale symmetries that exist in these webs. Certain eigenvectors of the Jacobian describing dynamical modes of the system, such as specific instabilities or responses to perturbations, localize on these symmetric motifs. On the one hand this means that by removing a symmetry from the network one obtains a system which has identical dynamics except for the removal of the localized mode. This explains the previously observed equivalence. On the other hand it means that we can identify dynamical modes that only depend on the symmetric motif. Symmetric structures thus provide an example for mesoscale network motifs having distinct and exact implications for the dynamics.
AB - A present challenge in complex systems is to identify mesoscale structures that have distinct dynamical implications. In this paper we present a detailed investigation of a previously observed dynamical equivalence of certian ecological food webs. We show that this equivalence is rooted in mesoscale symmetries that exist in these webs. Certain eigenvectors of the Jacobian describing dynamical modes of the system, such as specific instabilities or responses to perturbations, localize on these symmetric motifs. On the one hand this means that by removing a symmetry from the network one obtains a system which has identical dynamics except for the removal of the localized mode. This explains the previously observed equivalence. On the other hand it means that we can identify dynamical modes that only depend on the symmetric motif. Symmetric structures thus provide an example for mesoscale network motifs having distinct and exact implications for the dynamics.
U2 - 10.1088/1367-2630/14/10/105014
DO - 10.1088/1367-2630/14/10/105014
M3 - Article (Academic Journal)
VL - 14
JO - New Journal of Physics
JF - New Journal of Physics
SN - 1367-2630
M1 - 105014
ER -