Abstract
A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global phenomenon, nor is it simple to design a system that will exhibit some desired global property using only local knowledge. Here we propose a methodology that allows for the identification of local interactions that give rise to a desired global property of a network, the degree distribution. Given a set of observable processes acting on a network, we determine the conditions that must be satisfied to generate a desired steady-state degree distribution. We thereby provide a simple example for a class of tasks where a system can be designed to self-organize to a given state.
Highlights
C OMPLEX systems can exhibit phenomena and properties that are not inherent in the system’s constituents but arise from their interactions
While in biology self-organization is essential for the function, it often appears in technical systems primarily as a source of failure
We describe the evolution of the network using a heterogeneous activeneighbourhood approximation [16], [30], which tracks the evolution of nodes in a specific state and the number of neighbours it has in each state
Summary
C OMPLEX systems can exhibit phenomena and properties that are not inherent in the system’s constituents but arise from their interactions. Ordered structures can be formed without requiring pre-appointed hubs or leaders [1]. In biology the ability of complex systems to form macroscopic structures and patterns based on simple local rules is evident in all organisms and on all levels of organization. Examples range from the formation of complex (bio)molecules from simple chemical reactions, via the development of tissues and organisms, to social organization and collective decision-making [2]. Technical systems too provide many examples of self-organization, including particular types of powercuts [3], traffic jams [4], and structural instabilities in constructions [5]. While in biology self-organization is essential for the function, it often appears in technical systems primarily as a source of failure
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