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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 financial and social phenomena starting from geographical economics to macroeconomics and finance, and its goal is to provide readers an outline of a number of fascinating issues for learn at an intermediate point. 3 various and interdisciplinary, yet complementary, points of networks are prepare in one piece, specifically: (i) complicated networks concept, (ii) utilized community research to social and fiscal interrelations, and (iii) dynamical evolution of structures and networks. the amount contains contributions from very good students in economics and social sciences in addition to top specialists within the fields of complicated networks and nonlinear dynamics.

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New York Du WB, Cao XB, Hu MB (2009a) The effect of asymmetric payoff mechanism on evolutionary networked prisoner’s dilemma game. Phys A Stat Mech Appl 388(24):5005–5012 Du WB, Cao XB, Hu MB, Yang HX, Zhou H (2009b) Effects of expectation and noise on evolutionary games. Phys A Stat Mech Appl 388(11):2215–2220 Du WB, Cao XB, Zhao L, Hu MB (2009c) Evolutionary games on scale-free networks with a preferential selection mechanism. Phys A Stat Mech Appl 388(20):4509–4514 Elliott M, Golub B, Jackson MO (2014) Financial networks and contagion.

Ricoy-Riego, without whom this work would surely have not been done and life would be totally different. M. Varela and G. Rotundo References Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97 Albert R, Jeong H, Barabasi A (2000) Error and attack tolerance of complex networks. Nature 406(6794):378–382 Almeida-Neto M, Guimarães P, Guimarães Jr PR, Loyola RD, Ulrich W (2008) A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement.

This corollary is a direct application of Theorem 3. Notice that the diffusion threshold coincides for all the absolute adoption rules considered. Nevertheless, as described in López-Pintado (2008), for cases (a) and (b) the endemic state . / exhibits a second order phase transition at the diffusion threshold D . In other words, the endemic state . / is a continuous function of the spreading rate and, therefore, as converges to , . / converges to . /. For case (c), however, we obtain a discontinuity in the endemic fraction of adopters at D (first order phase transition or hysteresis) as illustrated in Fig.

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