Citation: Pan Yang, Jianwen Feng, Xinchu Fu. Cluster collective behaviors via feedback pinning control induced by epidemic spread in a patchy population with dispersal[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4718-4746. doi: 10.3934/mbe.2020259
[1] | H. Chen, P. Shi, C. C. Lim, Pinning impulsive synchronization for stochastic reaction-diffusion dynamical networks with delay, Neural Networks, 106 (2018), 281-293. |
[2] | W. H. Chen, Y. L. Liu, and W. X. Zheng, Synchronization analysis of two-time-scale nonlinear complex networks with time-scale-dependent coupling, IEEE Trans. Cybern., 49 (2019), 3255-3267. |
[3] | J. Q. Lu, J. D. Cao, Adaptive synchronization of uncertain dynamical networks with delayed coupling, Nonlinear Dyn., 53 (2008), 107-115. |
[4] | E. Panteley, A. Loria, Synchronization and dynamic consensus of heterogeneous networked systems, IEEE Trans. Autom. Contr., 62 (2017), 3758-3773. |
[5] | H. A. Tang, J. L. Wang, L. D. Wang, X. F. Hu, Y. Zhou, S. K. Duan, Impulsive control for passivity and exponential synchronization of coupled neural networks with multiple weights, J. Franklin Inst., 356 (2019), 5434-5463. |
[6] | C. Castellano and R. Pastor-Satorras, Thresholds for epidemic spreading in networks, Phys. Rev. Lett., 105 (2010), 218701. |
[7] | H. Guo, M. Y. Li, Z. Shuai, Global dynamics of a general class of multistage models for infectious diseases, SIAM J. Appl. Math., 72 (2012), 261-279. |
[8] | M. Kitsak, L. K. Gallos, S. Havlin, F. Liljeros, L. Muchnik, H. Eugene Stanley, et al., Identification of influential spreaders in complex networks, Nat. Phys., 6 (2010), 888-893. |
[9] | L. Lü, D. Chen, T. Zhou, The small world yields the most effective information spreading, New J. Phys., 13 (2011), 123005. |
[10] | H. T. Song, S. Q. Liu, W. H. Jiang, Global dynamics of amultistage sir model with distributed delays and nonlinear incidence rate, Math. Methods Appl. Sci., 40 (2017), 2153-2164. |
[11] | C. L. Apicella, F. W. Marlowe, J. H. Fowler, N. A. Christakis, Social networks and cooperation in hunter-gatherers, Nature, 481 (2012), 497-501. |
[12] | A. L. Barábasi, R. Albert, Emerhence of sclaing in random networks, Science, 286 (1999), 509-512. |
[13] | A. C. Linked, How everything is connected to everything else and what it means for business, science, and everyday life, Math. Comput. Edu., 43 (2009), 271-272. |
[14] | P. Dodds, R. Muhamad, D. Watts, An experimental study of search in global social networks, Science, 301 (2003), 827-829. |
[15] | H. Dong, N. Hou, Z. Wang, W. Ren, Variance-constrained state estimation for complex networks with randomly varying topologies, IEEE Trans. Neural Networks Learn. Syst., 29 (2018), 2757-2768. |
[16] | M. Granovetter, The strength of weak ties, Am. J. Sociol., 78 (1973), 1360-1380. |
[17] | S. Milgram, The small world problem, Psychol. Today, 2 (1967), 60-67. |
[18] | L. Stella, D. Bauso, Bio-inspired evolutionary dynamics on complex networks under uncertain cross-inhibitory signals, Automatica, 100 (2019), 61-66. |
[19] | D. J. Watts, S. H. Strogatz, Collective dynamics of small-world networks, Nature, 393 (1998), 440-442. |
[20] | W. L. Zhang, X. S. Yang, C. D. Li, Fixed-time stochastic synchronization of complex networks via continuous control, IEEE T. Cybern., 49 (2019), 3099-3104. |
[21] | S. P. Ansari, S. K. Agrawal, S. Das, Stability analysis of fractiona-lorder generalized chaotic susceptible-infected-recovered epidemic model and its synchronization using active control method, Pramana, 84 (2015), 23-32. |
[22] | E. Arceo-May, C. F. Moukarzel, Synchronization and extinction in a high-infectivity spatial sirs with long-range links, J. Stat. Mech. Theory Exp., 2019 (2019), 013203. |
[23] | Z. L. Tang, S. M. Li, Epidemic model based security analysis of firefly clock synchronization in wireless sensor networks, Int. J. Security Appl., 9 (2015), 19-34. |
[24] | D. G. Xu, X. Y. Xu, C. H. Yang, W. H. Gui, Spreading dynamics and synchronization behavior of periodic diseases on complex networks, Phys. A, 466 (2017), 544-551. |
[25] | G. Yan, Z. Fu, J. Ren, W. X. Wang, Collective synchronization induced by epidemic dynamics on complex networks with communities, Phys. Rev. E, 75 (2007), 016108. |
[26] | K. Z. Li, X. C. Fu, M. Small, Z. J. Ma, Adaptive mechanism between dynamical synchronization and epidemic behavior on complex networks, Chaos, 21 (2011), 033111. |
[27] | K. Z. Li, Z. J. Ma, Z. Jia, M. Small, X. C. Fu, Interplay between collective behavior and spreading dynamics on complex networks, Chaos, 22 (2012), 043113. |
[28] | M. F. Sun, Y. J. Lou, J. Q. Duan, and X. C. Fu, Behavioral synchronization induced by epidemic spread in complex networks, Chaos, 27 (2017), 063101. |
[29] | M. F. Sun, M. Small, S. S. Lee, X. C. Fu, An exploration and simulation of epidemic spread and its control inmultiplex networks, SIAM J. Appl. Math., 78 (2018), 1602-1631. |
[30] | S. M. Cai, F. L. Zhou, Q. B. He,Fixed-time cluster lag synchronization in directed heterogeneous community networks, Phys. A, 525 (2019), 128-142. |
[31] | F. B. Li, Z. J. Ma, Q. C. Duan, Clustering component synchronization in a class of unconnected networks via pinning control, Phys. A, 525 (2019), 394-401. |
[32] | Z. P. Xu, K. Z. Li, M. F. Sun, and X. C. Fu, Interaction between epidemic spread and collective behavior in scale-free networks with community structure, J. Theor. Biol., 462 (2019), 122-133. |
[33] | J. Li, X. Zou, Dynamics of an epidemic model with non-local infections for diseases with latency over a patchy environment, J. Math. Biol., 60 (2010), 645-686. |
[34] | M. Y. Li, Z. S. Shuai, Global stablity of an epidemic model in a patchy environment, Can. Appl. Math. Q., 17 (2009), 175-187. |
[35] | P. Yang, Z. P. Xu, J. W. Feng, and X. C. Fu, Feedback pinning control of collective behaviors aroused by epidemic spread on complex networks, Chaos, 29 (2019), 033122. |
[36] | X. S. Yang, J. D. Cao, Adaptive pinning synchronization of complex networks with stochastic perturbations, Discrete Dyn. Nat. Soc., 2010 (2010), 416182. |
[37] | J. Y. Wang, J. W. Feng, C. Xu, Y. Zhao, and J. Q. Feng, Pinning synchronization of nonlinearly coupled complex networks with time-varying delays using m-matrix strategies, Neurocomputing, 177 (2016), 89-97. |
[38] | A. Berman, R. J. Plemmom, Nonnegative matrices in the mathematical sciences, Academic Press, New York, 1979. |
[39] | M. Y. Li, Z. S. Shuai, Global-stability problem for coupled systems of differential equations on networks, J. Differ. Equation, 248 (2010), 1-20. |
[40] | D. M. Li, J. A. Lu, X. Q. Wu, G. R. Chen, Estimating the ultimate bound and positively invariant set for the lorenz system and a unified chaotic system, J. Math. Anal. Appl., 323 (2006), 844-853. |
[41] | J. Y. Wang, J. W. Feng, C. Xu, Y. Zhao, Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix, Nonlinear Dyn., 67 (2012), 1635-1646. |