Ref Scale Free Topologies and Robust Networks

Aldana, M. (2003). Boolian dynamics of networks with scale free topology. Physica D 185: 45-66. (In a scale-free network, the proportion of nodes P(k) having k links decays as a power law whose exponent is about 2-3. Existence of a phase transition occurs for values of scale-free exponent in the open interval 2-2.5. Fine-tuning that is usually required for stability in Boolian networks having random topology is unnecessary if the topology of the network is scale free.)

Robust Networks: Aldana, M. and P. Cluzel (2003). A natural class of robust networks. PNAS 100(15): 8710-8714. (These authors present a prototype for studying dynamical systems predicting the robustness of networks against varying parameters, demonstrating that dynamical robustness of complex networks is a consequence of their scale-free topology and in contrast, networks having homogeneous random topologies require fine-tuning of their internal parameters to sustain dynamical activity that remains stable.)

Pesin, Y. B. (1997). Dimension Theory in Dynamical Systems: Contemporary Views and Applications. Chicago Lectures in Mathematics, University of Chicago Press, Chicago. (This book is neither about dimensional theory or dynamical systems theory but covers subjects at the intersection of these two fields formulated within the last fifteen years.)

Baddi, R. and A. Politi (1997). Complexity: Hierarchical Structures and Scaling in Physics. Cambridge University Press, Cambridge. (This book provides a comprehensive discussion of complexity in physical, chemical and biological systems as well as in mathematical models to emphasize their common features by employing a uniform mathematical description with many examples.)

0 0

Post a comment