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Sentiment cycles in discrete-time homogeneous networks

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  • Gomes, Orlando

Abstract

Consider a network connecting individual agents that are endowed with distinct sentiments or ‘views of the world’. Specifically, assume that each node in the network contains an agent that, at a given period t, can be found in one of five states: sentiment neutrality, exuberant optimism, non-exuberant optimism, exuberant pessimism and non-exuberant pessimism. Local interaction rules, similar to those one encounters in rumor propagation models, make agents change their sentiment as they contact with others. Under a continuous-time framework, the proposed setting delivers a stable fixed-point equilibrium, meaning that the shares of agents in each sentiment category will converge to constant steady-state levels. The inspection of the same structure of analysis in discrete-time indicates that the stability outcome continues to hold when the connectivity degree is equal to 1. However, this result might change as one considers higher-order connectivity. In this last case, persistent endogenous waves of optimism and pessimism emerge under a reasonable parameterization of the model.

Suggested Citation

  • Gomes, Orlando, 2015. "Sentiment cycles in discrete-time homogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 224-238.
    • Handle: RePEc:eee:phsmap:v:428:y:2015:i:c:p:224-238
    DOI: 10.1016/j.physa.2015.01.084
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    References listed on IDEAS

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    1. Nekovee, M. & Moreno, Y. & Bianconi, G. & Marsili, M., 2007. "Theory of rumour spreading in complex social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 457-470.
    2. Zhao, Laijun & Wang, Jiajia & Huang, Rongbing & Cui, Hongxin & Qiu, Xiaoyan & Wang, Xiaoli, 2014. "Sentiment contagion in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 17-23.
    3. Zhao, Laijun & Wang, Jiajia & Chen, Yucheng & Wang, Qin & Cheng, Jingjing & Cui, Hongxin, 2012. "SIHR rumor spreading model in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2444-2453.
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    Cited by:

    1. Orlando Gomes & J. C. Sprott, 2017. "Sentiment-driven limit cycles and chaos," Journal of Evolutionary Economics, Springer, vol. 27(4), pages 729-760, September.
    2. Argentiero, Amedeo & Bovi, Maurizio & Cerqueti, Roy, 2016. "Bayesian estimation and entropy for economic dynamic stochastic models: An exploration of overconsumption," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 143-157.

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