Abstract

ABSTRACT Complex systems, from the Internet to the brain, remain as the last pending challenges for science. Because of their intricate structure and dynamics, such systems are unlikely to disclose their secrets to simpler scientific approaches such as linear system analysis. More sophisticated and effective concepts and methods are required in order to tackle those problems. Because of their generality [1], complex networks represent a natural alternative for representing, characterizing and modeling the structure and non-linear dynamics of all discrete complex systems [2]. In this talk, I will describe recent developments aimed at characterizing and relating the structure and dynamics of complex systems represented by complex networks. The talk will start by addressing the subject of systematic characterization of connectivity and dynamics in complex systems [1]. Next, these concepts are illustrated with respect to complex systems underlain by geometry, including morphological neuronal networks [3]. I will also present the recently introduced concept of superedges [4] – an approach which natural and comprehensively integrates the topology and dynamics of a given complex system, as well as the concept of avalanches of activations in complex systems [5] and how they can be modeled in terms of concentric representations of complex network. Among the presented results, we have the fact that the occurrence of avalanches is intrinsically related to the hierarchical organization of the network as well as to the presence of long range connections. It will also be shown that the dynamics of avalanches can be used to identify modularity in complex networks [6]. Dynamical complex systems with dynamical topology and moving nodes will also be addressed [7].

Basic References:

[1] – Characterization of complex networks: A survey of measurements (http://arxiv.org/abs/cond-mat/0505185). Advances in Physics, 56, 167 (2007).

[2] – Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications (http://arxiv.org/abs/0711.3199).

[3] – Morphological complex networks: Can individual morphology determine the general connectivity and dynamics of networks? (http://arxiv.org/abs/q-bio/0503041).

[4] – Superedges: Connecting Structure and Dynamics in Complex Networks (http://arxiv.org/abs/0801.4068).

[5] – Modeling the concentric organization of lattices and path-regular networks and Its Application to Complex Neuronal Networks Analysis (http://hal.archives-ouvertes.fr/hal-00258893/en/).

[6] – Activation Confinement inside Complex Networks Communities (http://arxiv.org/abs/0802.1272).

[7] – 2D pattern evolution constrained by complex networks dynamics (http://arxiv.org/abs/physics/0610001).

LDFC thanks FAPESP , CNPq, CAPES and St Catharine’s College (Univ. of Cambridge) for support.