Rui Vilela Mendes

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A four-node network consisting of a negative circuit controlling a positive one is studied. It models some of the features of the p53 gene network. Using piecewise linear dynamics with thresholds, the allowed dynamical classes are fully characterized and coded. The biologically relevant situations are identified and conclusions drawn concerning the(More)
Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these networks. Here a dynamical approach is used to characterize the small-world phenomenon. Using the β−model, a coupled map(More)
—The immune system is a cognitive system of complexity comparable to the brain and its computational algorithms suggest new solutions to engineering problems or new ways of looking at these problems. Using immunological principles, a two-(or three-) module algorithm is developed which is capable of launching a specific response to an anomalous situation for(More)
—Formal language techniques have been used in the past to study autonomous dynamical systems. However, for controlled systems, new features are needed to distinguish between information generated by the system and input control. We show how the modeling framework for controlled dynamical systems leads naturally to a formulation in terms of context-dependent(More)
Networks have been studied mainly by statistical methods which emphasize their topological structure. Here, one collects some mathematical tools and results which might be useful to study both the dynamics of agents living on the network and the networks themselves as evolving dynamical systems. They include decomposition of differential dynamics, ergodic(More)
Formal language techniques have been used in the past to study autonomous dynamical systems. However, for controlled systems, new features are needed to distinguish between information generated by the system and input control. We show how the modelling framework for controlled dynamical systems leads naturally to a formulation in terms of context-dependent(More)