Symmetric and Asymmetric Tendencies in Stable Complex Systems.

ABSTRACT: A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor mutualistic and competitive relationships that are asymmetrical (non-reciprocative) and trophic relationships that are symmetrical (reciprocative). Additionally, we define a measure called the interdependence diversity that quantifies how distributed the dependencies are between the dynamical variables in the system. We find that increasing interdependence diversity has a destabilizing effect on the equilibrium point, and the effect is greater for trophic relationships t

SUBMITTER: Tan JP 

PROVIDER: S-EPMC4992841 | biostudies-literature | 2016 Aug

REPOSITORIES: biostudies-literature