[1] M. R. Gardner and W. R. Ashby, Connectance of large dynamic (cybernetic) systems: critical values for stability. Nature 228, 784–784 (1970).
[2] R. M. May, Will a large complex system be stable? Nature 238, 413–414 (1972).
[3] S. Allesina and S. Tang, Stability criteria for complex ecosystems. Nature 483, 205–208 (2012).
[4] Pimm, S. L. Complexity and stability: another look at MacArthur’s original hypothesis. OIKOS 33, 351–357 (1979).
[5] E. Beninc`a, J. Huisman, R. Heerkloss, K. D. J¨ohnk, P. Branco, E. H. Van Nes, M. Scheffer, and S. P. Ellner, Chaos in a long-term experiment with a plankton community. Nature 451, 822–825 (2008).
[6] P. Bak, and K. Sneppen, Punctuated equilibrium and criticality in a simple model of evolution. Phys. Rev. Lett. 71, 4083–4086 (1993).
[7] R. V. Sol´e and J. Bascompte, Are critical phenomena relevant to large-scale evolution? Proc. R. Soc. Lond. B 263, 161–168 (1996).
[8] R. Albert, H. Jeong, and A.-L. Barab´asi, Error and attack tolerance of complex networks. Nature 406, 378–82 (2000).
[9] D. J. Watts, A simple model of global cascades on random networks. PNAS 99, 5766– 5771 (2002).
[10] A. A. Moreira, J. S. Andrade, H. J. Herrmann, and O. I. Joseph, How to make a fragile network robust and vice versa. Phys. Rev. Lett. 102, 018701 (2009).
[11] S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, and S. Havlin, Catastrophic cascade of failures in interdependent networks. Nature 464, 1025–1028 (2010).
[12] H. J. Herrmann, C. M. Schneider, A. A. Moreira, J. S. Andrade, and S. Havlin, Onion- like network topology enhances robustness against malicious attacks. J. Stat. Mech. 2011, P01027 (2011).
[13] P. J. Taylor, Consistent scaling and parameter choice for linear and generalized Lotka- Volterra models used in community ecology. J. theor. Biol. 135, 543–568 (1988).
[14] P. J. Taylor, The construction and turnover of complex community models having gen- eralized Lotka-Volterra dynamics. J. theor. Biol. 135, 569–588 (1988).
[15] K. Tokita and A. Yasutomi, Mass extinction in a dynamical system of evolution with variable dimension. Phys. Rev. E 60, 842–847 (1999).
[16] T. Shimada, A universal transition in the robustness of evolving open systems. Scientific Reports 4 4082 (2014).
[17] F. Ogushi, Kert´esz, K. Kaski, and T. Shimada, Enhanced robustness of evolving open systems by the bidirectionality of interactions between elements. Scientific Reports 7, 6978 (2017).
[18] F. Ogushi, Kert´esz, K. Kaski, and T. Shimada, Temporal inactivation enhances robust- ness in an evolving system. J. of Royal Society Open Science 6, 181471 (2019).
[19] M. C. Mu¨nnix, T. Shimada, R. Scha¨fer, F. Leyvraz, T. H. Seligman, Thomas Guhr, and H. Eugene Stanley Identifying states of a financial market. Scientific Reports 2, 644 (2012).
[20] F. Ogushi, Kert´esz, K. Kaski, and T. Shimada, Ecology in the digital world of Wikipedia. arXiv:2105.10333
[21] R. Albert and A.-L. Barab´asi, Statistical Mechanics of Complex Networks. Rev. Mod. Phys. 74, 47 (2002).
[22] T. C. Ings et al., Ecological networks – beyond food webs. J. Animal Ecology 78, 253–69 (2009).
[23] T. Shimada, S. Yukawa, and N. Ito, Life-span of families in fossil data forms q-exponential distribution. Int. J. Mod. Phys. C 14, 1267–1271 (2003).
[24] Y. Murase, T. Shimada, and N. Ito, A simple model for skewed species-lifetime distribu- tions. New J. of Physics 12, 063021 (2010).
[25] T. Mizuno, and M. Takayasu, The statistical relationship between product life cycle and repeat purchase behavior in convenience stores. Prog. Theor. Phys. Suppl. 179, 71–79 (2009).
[26] W. Miura, H. Takayasu, and M. Takayasu, Effect of coagulation of nodes in an evolving complex network. Phys. Rev. Lett. 108, 168701 (2012).
[27] M. I. G. Daepp, M. J. Hamilton, G. B. West, and L. M. A. Bettencourt, The mortality of companies. J. of Royal Society Interface 12, 20150120 (2015).
[28] T. Shimada, A Universal Mechanism of Determining the Robustness of Evolving Systems. in Mathematical Approaches to Biological Systems, 95–117 (Springer, 2015).
論文の公開元へ
