Simulating the Spreading of Two Competing Public Opinion Information on Complex Network

ABSTRACT

In this paper, we investigate the regularity of spreading of information and public opinions towards two competing products in complex networks. By building its mathematical model and simulating its evolution process, we have found the statistical regularity for support rates of two different products at a steady stage. The research shows that strength of the public opinion spreading is proportional to the final support rates of a product.

In this paper, we investigate the regularity of spreading of information and public opinions towards two competing products in complex networks. By building its mathematical model and simulating its evolution process, we have found the statistical regularity for support rates of two different products at a steady stage. The research shows that strength of the public opinion spreading is proportional to the final support rates of a product.

Cite this paper

M. Xie, Z. Jia, Y. Chen and Q. Deng, "Simulating the Spreading of Two Competing Public Opinion Information on Complex Network,"*Applied Mathematics*, Vol. 3 No. 9, 2012, pp. 1074-1078. doi: 10.4236/am.2012.39158.

M. Xie, Z. Jia, Y. Chen and Q. Deng, "Simulating the Spreading of Two Competing Public Opinion Information on Complex Network,"

References

[1] R. Albert, H. Jeong and A. L. Barabási, “Diameter of the World-Wide Web,” Nature, Vol. 401, 1999, pp. 130-131. doi:10.1038/43601

[2] P. Sen, P. Dasgupta, A. Chatterjee, et al., “Small-Word Properties of the Indian Railway Network,” Physical Review E, Vol. 67, 2003, Article ID: 036106. doi:10.1103/PhysRevE.67.036106

[3] T. Xu, J. Chen, Y. He, et al., “Complex Networks Properties of Chinese Power Grid,” International Journal of Modern Physics B, Vol. 18, 2004, pp. 2599-2603. doi:10.1142/S0217979204025749

[4] F. Liljeros, C. R. Edling, L. A. N. Amaral, et al., “The Web of Human Sexual Contact,” Nature, Vol. 411, 2001, pp. 907-908. doi:10.1038/35082140

[5] M. E. J. Newman, “Scientific Collaboration Networks. I. Network Construction and Fundamental Results,” Physical Review E, Vol. 64, 2001, Article ID: 016131.

[6] J. Hu, S. Zhong and L. Liang, “Exponential Stability Analysis of Stochastic Delayed Cellular Neural Network,” Chaos, Solitons & Fractals, Vol. 27, No. 4, 2006, pp. 1006-1010. doi:10.1016/j.chaos.2005.04.067

[7] J. A. Dunne, R. J. Williams and N. D. Martinez, “Network Structure and Biodiversity Loss in Food Webs: Robustness Increases with Connectance,” Ecology Letters, Vol. 5, No. 4, 2002, pp. 558-567. doi:10.1046/j.1461-0248.2002.00354.x

[8] T. Zhou, Z. Fu and B. Wang, “Epidemic Dynamics on Complex Network,” Progress in Natural Science, Vol. 16, No. 5, 2006, pp. 452-457. doi:10.1080/10020070612330019

[9] X. J. Xu, H. O. Peng, X. M. Wang, et al., “Epidemic Spreading with Time Delay in Complex Networks,” Physica A, Vol. 367, 2006, pp. 525-530. doi:10.1016/j.physa.2005.11.035

[10] K. Li, M. Small, H. Zhang, et al., “Epidemic Outbreaks on Networks with Effective Contacts,” Nonlinear Analysis: Real World Application, Vol. 11, No. 2, 2010, pp. 1017-1025. doi:10.1016/j.nonrwa.2009.01.046

[11] R. Pastor-Satorras and A. Vespingnani, “Epidemic Spreading in Scale-Free Networks,” Physical Review Letters, Vol. 86, No. 4, 2001, pp. 3200-3203.

[12] B. Wang and T. Zhou, “Several Directions in Complex System Research,” Complex Systems and Complexity Science, Vol. 5, No. 4, 2008, pp. 21-28.

[13] J. M. Bristor, “Enhanced Explanations of Word of Mouth Communications: The Power of Relationships,” Research in Consumer Behavior, Vol. 4, 1990, pp. 51-83.

[14] A. Grabowski and R. A. Kosiński, “Ising-Based Model of Opinion Formation in a Complex Network of Interpersonal Interactions,” Physica A, Vol. 361, No. 2, 2006, pp. 651-664. doi:10.1016/j.physa.2005.06.102

[15] M. E. J. Newman, “Threshold Effects for Two Pathogens Spreading on a Network,” Physical Review Letters, Vol. 95, No. 108701, 2005.

[16] P. Erd?s and A. Rényi, “On Random Graphs I,” Publicationes Mathematicae Debrecen, Vol. 6, 1959, pp. 290297.

[17] D. J. Watts and S. H. Strogatz, “Collective Dynamics of ‘Small-World’ Networks,” Nature, Vol. 393, 1998, pp. 440-442. doi:10.1038/30918

[18] A. L. Barabási and R. Albert, “Emergence of Scaling in Random Networks,” Science, Vol. 286, No. 5439, 1999, pp. 509-512. doi:10.1126/science.286.5439.509

[1] R. Albert, H. Jeong and A. L. Barabási, “Diameter of the World-Wide Web,” Nature, Vol. 401, 1999, pp. 130-131. doi:10.1038/43601

[2] P. Sen, P. Dasgupta, A. Chatterjee, et al., “Small-Word Properties of the Indian Railway Network,” Physical Review E, Vol. 67, 2003, Article ID: 036106. doi:10.1103/PhysRevE.67.036106

[3] T. Xu, J. Chen, Y. He, et al., “Complex Networks Properties of Chinese Power Grid,” International Journal of Modern Physics B, Vol. 18, 2004, pp. 2599-2603. doi:10.1142/S0217979204025749

[4] F. Liljeros, C. R. Edling, L. A. N. Amaral, et al., “The Web of Human Sexual Contact,” Nature, Vol. 411, 2001, pp. 907-908. doi:10.1038/35082140

[5] M. E. J. Newman, “Scientific Collaboration Networks. I. Network Construction and Fundamental Results,” Physical Review E, Vol. 64, 2001, Article ID: 016131.

[6] J. Hu, S. Zhong and L. Liang, “Exponential Stability Analysis of Stochastic Delayed Cellular Neural Network,” Chaos, Solitons & Fractals, Vol. 27, No. 4, 2006, pp. 1006-1010. doi:10.1016/j.chaos.2005.04.067

[7] J. A. Dunne, R. J. Williams and N. D. Martinez, “Network Structure and Biodiversity Loss in Food Webs: Robustness Increases with Connectance,” Ecology Letters, Vol. 5, No. 4, 2002, pp. 558-567. doi:10.1046/j.1461-0248.2002.00354.x

[8] T. Zhou, Z. Fu and B. Wang, “Epidemic Dynamics on Complex Network,” Progress in Natural Science, Vol. 16, No. 5, 2006, pp. 452-457. doi:10.1080/10020070612330019

[9] X. J. Xu, H. O. Peng, X. M. Wang, et al., “Epidemic Spreading with Time Delay in Complex Networks,” Physica A, Vol. 367, 2006, pp. 525-530. doi:10.1016/j.physa.2005.11.035

[10] K. Li, M. Small, H. Zhang, et al., “Epidemic Outbreaks on Networks with Effective Contacts,” Nonlinear Analysis: Real World Application, Vol. 11, No. 2, 2010, pp. 1017-1025. doi:10.1016/j.nonrwa.2009.01.046

[11] R. Pastor-Satorras and A. Vespingnani, “Epidemic Spreading in Scale-Free Networks,” Physical Review Letters, Vol. 86, No. 4, 2001, pp. 3200-3203.

[12] B. Wang and T. Zhou, “Several Directions in Complex System Research,” Complex Systems and Complexity Science, Vol. 5, No. 4, 2008, pp. 21-28.

[13] J. M. Bristor, “Enhanced Explanations of Word of Mouth Communications: The Power of Relationships,” Research in Consumer Behavior, Vol. 4, 1990, pp. 51-83.

[14] A. Grabowski and R. A. Kosiński, “Ising-Based Model of Opinion Formation in a Complex Network of Interpersonal Interactions,” Physica A, Vol. 361, No. 2, 2006, pp. 651-664. doi:10.1016/j.physa.2005.06.102

[15] M. E. J. Newman, “Threshold Effects for Two Pathogens Spreading on a Network,” Physical Review Letters, Vol. 95, No. 108701, 2005.

[16] P. Erd?s and A. Rényi, “On Random Graphs I,” Publicationes Mathematicae Debrecen, Vol. 6, 1959, pp. 290297.

[17] D. J. Watts and S. H. Strogatz, “Collective Dynamics of ‘Small-World’ Networks,” Nature, Vol. 393, 1998, pp. 440-442. doi:10.1038/30918

[18] A. L. Barabási and R. Albert, “Emergence of Scaling in Random Networks,” Science, Vol. 286, No. 5439, 1999, pp. 509-512. doi:10.1126/science.286.5439.509