Reaction-diffusion processes on interconnected scale-free networks

Abstract

We study the two particle annihilation reaction A + B → ∅ on interconnected scale free networks, using different interconnecting strategies. We explore how the mixing of particles and the process evolution are influenced by the number of interconnecting links, by their functional properties, and by the interconnectivity strategies in use. We show that the reaction rates on this system are faster than what was observed in other topologies, due to the better particle mixing which suppresses the segregation effect, inline with previous studies performed on single scale free networks.Using complex networks to describe real systems is becoming standard practice [1, 2], but, understanding how networks interact in an increasingly interconnected world [3] is an open challenge for network science. Networks in general retain their identity despite the existence of interconnections, for example a communication network does not change its role when it is connected to a power network. This makes our knowledge about isolated networks relevant for the interconnected case. However, there exist network properties that are strongly affected by interconnectivity [4][5][6][7][8][9][10][11] In addition, interconnecting links may be different (with respect to their function) than the normal links within the networks. In the example at hand, via interconnecting links we provide power to the communication network, and we control how the load is distributed in the power network. Thus, failure of these links has severe consequences, which is why in this case they are called dependency links [12]. In such cases extra care should be taken, and interconnected networks should not be studied as isolated networks with distinct communities. Indeed, recently it was shown that an interconnected system of networks may be either in a regime where the various networks are structurally independent, or in a regime where they are strongly coupled and the system behaves like one large network [13,14]. This can influence at large the evolution of dynamical processes on such systems.In this work we provide a detailed numerical study of how interconnectivity affects the evolution of a diffusion-reaction dynamical process, when the reaction evolves on an interconnected network substrate. More precisely, we study the reaction rates of the annihilation reaction A + B → ∅ on coupled Scale Free Networks (SFN) using different interconnecting strategies.

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