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Complex evolving systems such as the biosphere, ecosystems and societies exhibit sudden collapses, for reasons that are only partially understood. Here we study this phenomenon using a mathematical model of a system that evolves under Darwinian selection and exhibits the spontaneous growth, stasis and collapse of its structure. We find that the typical lifetime of the system increases sharply with the diversity of its components or species. We also find that the prime reason for crashes is a naturally occurring internal fragility of the system. This fragility is captured in the network organizational character and is related to a reduced multiplicity of pathways between its components. This work suggests new parameters for understanding the robustness of evolving molecular networks, ecosystems, societies, and markets.
In this paper, the synchronization in a hyper-network of coupled dynamical systems is investigated for the first time. An evolving hyper-network model is proposed for better describing some complex systems. A concept of joint degree is introduced, an
I analyse a model of an evolving network represented as a directed graph; each node corresponds to one molecular species and the links to catalytic interactions between species. Over short timescales the graph remains fixed while relative populations
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be non-trivial. The st
We study the consequences of introducing individual nonconformity in social interactions, based on Axelrods model for the dissemination of culture. A constraint on the number of situations in which interaction may take place is introduced in order to
Behavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized--and thus homogeneous--across the network, previous work