By Pasquale Commendatore, Mariano Matilla-García, Luis M. Varela, Jose S. Cánovas
This quantity sheds mild at the present nation of complicated networks and nonlinear dynamics utilized to the knowledge of monetary and social phenomena starting from geographical economics to macroeconomics and finance, and its function is to offer readers an summary of a number of attention-grabbing subject matters for learn at an intermediate point. 3 assorted and interdisciplinary, yet complementary, points of networks are prepare in one piece, particularly: (i) advanced networks concept, (ii) utilized community research to social and fiscal interrelations, and (iii) dynamical evolution of platforms and networks. the quantity comprises contributions from very good students in economics and social sciences in addition to major specialists within the fields of advanced networks and nonlinear dynamics.
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Additional info for Complex Networks and Dynamics: Social and Economic Interactions
1 The SIS Model and Unbiased-Degree Random Networks In this section we focus on the unbiased-degree network case which represents the simplest framework to study random interactions characterized by a degree distribution. Let us first introduce some notation. t/ be the total frequency of active agents in the population at time t. t/ as a function of the parameters of the SIS model. t/). t/. Thus, the probability that a 32 D. t/. t/ D 0 for all d. Therefore, for each d, d D d ; 1C d where D ı is the (effective) spreading rate.
The diffusion threshold is D 1, both for the unbiased-degree and biased-degree random network. The reason is that, in this case, all agents have the same probability of becoming an adopter, independently of their degree. To see this, consider two agents i and j where i has degree d and j has degree 2d. It is straightforward to show that the probability that agent i observes a active agents in the sample coincides with the probability that agent j observes 2a. Moreover, the Imitation model assumes that both agents, i 2a and j, would have the same probability of adopting as da D 2d ).
0/. a/ for a > 1 does not appear in the condition is that in the initial periods of the dynamics there is only a small fraction of adopters in the population and, thus, the probability that an agent observes more than one adopter in her sample is negligible. , whether it is a second order phase transition or not). The results obtained for the Imitation model are striking. The diffusion threshold is D 1, both for the unbiased-degree and biased-degree random network. The reason is that, in this case, all agents have the same probability of becoming an adopter, independently of their degree.