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Codimension-Two Bifurcation, Chaos and Control in a Discrete-Time Information Diffusion Model

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Abstract

In this paper, we present a discrete model to illustrate how two pieces of information interact with online social networks and investigate the dynamics of discrete-time information diffusion model in three types: reverse type, intervention type and mutualistic type. It is found that the model has orbits with period 2, 4, 6, 8, 12, 16, 20, 30, quasiperiodic orbit, and undergoes heteroclinic bifurcation near 1:2 point, a homoclinic structure near 1:3 resonance point and an invariant cycle bifurcated by period 4 orbit near 1:4 resonance point. Moreover, in order to regulate information diffusion process and information security, we give two control strategies, the hybrid control method and the feedback controller of polynomial functions, to control chaos, flip bifurcation, 1:2, 1:3 and 1:4 resonances, respectively, in the two-dimensional discrete system.

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Acknowledgments

This work is supported by the NSFC (11271339) Project, the Plan for Scientific Innovation Talent of Henan Province (164200510011) and Innovative Research Team of Science and Technology in Henan Province (17IRTSTHN007).

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Correspondence to Jingli Ren.

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Communicated by Ferdinand Verhulst.

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Ren, J., Yu, L. Codimension-Two Bifurcation, Chaos and Control in a Discrete-Time Information Diffusion Model. J Nonlinear Sci 26, 1895–1931 (2016). https://doi.org/10.1007/s00332-016-9323-8

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