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Register a new userDiversity Begets Stability in an Evolving Network
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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.
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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, and the evolving mechanism of hyper-network is given with respect to the joint degree. The hyper-degree distribution of the proposed evolving hyper-network is derived based on a rate equation method and obeys a power law distribution. Furthermore, the synchronization in a hyper-network of coupled dynamical systems is investigated for the first time. By calculating the joint degree matrix, several simple yet useful synchronization criteria are obtained and illustrated by several numerical examples.
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 of the molecular species change according to a set of coupled differential equations. Over long timescales the system is subject to periodic perturbations, each of which adds one new node to the graph, with random links to other nodes, and removes one node with the least relative population. Starting from a sparse random graph, a small autocatalytic set (ACS) inevitably forms and then grows by accreting nodes until it spans the entire graph. The resultant fully autocatalytic graph, whose probability of forming by pure chance is very small, nevertheless forms in this model in an average time that grows only logarithmically with the size of the system. ACSs can also get destroyed, often accompanied by the sudden extinction of a large number of species. I show that the largest of the extinction events in this model are caused by one of three mechanisms, each of which produces a specific discontinuous change in the graphs topology. The model is analytically tractable: two theorems are proved which determine the set of nodes with least relative population in the attractor, for any given graph. This in turn can be used to analytically demonstrate the inevitability of the formation and growth of ACSs and calculate the associated timescales. Finally, I show that the formation and growth of ACSs is robust to the relaxation of many of the idealizations made to enhance the analytical tractability of the model.
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 structure of the network shows interesting hierarchical properties and in certain parameter regions the dynamics is polysynchronous: nodes can be divided in differently synchronized classes but contrary to cluster synchronization, nodes in the same class need not be connected to each other. These complicated synchrony patterns have been conjectured to play roles in systems biology and circuits. The adaptive system we study describes ways whereby this behaviour can evolve from undifferentiated nodes.
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 lift the unavoidable ho mogeneity present in the final configurations arising in Axelrods related models. The inclusion of this constraint leads to the occurrence of complex patterns of intracultural diversity whose statistical properties and spatial distribution are characterized by means of the concepts of cultural affinity and cultural cli ne. It is found that the relevant quantity that determines the properties of intracultural diversity is given by the fraction of cultural features that characterizes the cultural nonconformity of individuals.
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 suggests that the stability of synchronous states can be improved by making the generators homogeneous. Here, we show that a substantial additional improvement is possible by instead making the generators suitably heterogeneous. We develop a general method for attributing this counterintuitive effect to converse symmetry breaking, a recently established phenomenon in which the system must be asymmetric to maintain a stable symmetric state. These findings constitute the first demonstration of converse symmetry breaking in real-world systems, and our method promises to enable identification of this phenomenon in other networks whose functions rely on behavioral homogeneity.
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