Chaos in Heterogeneous Networks with Temporaly Inert Nodes J. J. Torres, J. Marro and S. de Franciscis Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y F´ ısica de la Materia University of Granada, Facultad de Ciencias, 18071 Granada, Spain July 24, 2007 Abstract We discuss an attractor neural network in which only a fraction ρ of nodes is simultaneously updated. In addition, the network has a het- erogenous distribution of connection weights and, depending on the current degree of order, connections are changed at random by a factor Φ on short–time scales. The resulting dynamic attractors may become unstable in a certain range of Φ thus ensuing chaotic itineracy which highly depends on ρ. For intermediate values of ρ, we observe that the number of attractors visited increases with ρ, and that the trajectory may change from regular to chaotic and vice versa as ρ is modified. Statistical analysis of time series shows a power–law spectra under conditions in which the attractors’ space is most efficiently explored. PACS: 05.45.Pq; 05.50.+q; 87.18.Sn; 87.23.Ge; 89.40.-a; 89.65.-s; 89.75.- k 1 Introduction There has been a great interest in the study of complex networks in physics [Barabasi, 2002; Boccaletti et al., 2006] mainly focusing on the wiring topol- ogy of the network. Natural and man–made networks exhibit a number of relevant qualities besides interesting topological structure [Boccaletti et al., 1