蔡超然

发表论文（*通讯、#共一）：

15) Chao-Ran Cai*, Yuan-Yuan Nie, and Petter Holme*, Epidemic criticality in temporal networks, Phys. Rev. Res. 6, L022017 (2024).

14) Xin Chang, Chao-Ran Cai*, Ji-Qiang Zhang, Wen-Li Yang, The universality of physical images at relative timescales on multiplex networks, Chaos Solitons Fractals 182, 114780 (2024).

13) Chao-Ran Cai*, Na-Na Liu, Xin Chang, and Xu-Sheng Liu, Physical images of relative timescales in coevolution dynamics, Phys. Rev. Res. 5, 033220 (2023). 

12) Zhen-Wei Ding#, Guo-Zhong Zheng, Chao-Ran Cai, Wei-Ran Cai, Li Chen, Ji-Qiang Zhang#, and Xu-Ming Wang*, Emergence of cooperation in two-agent repeated games with reinforcement  learning, Chaos Solitons Fractals 175, 114032 (2023).

11) Xin Chang, Chao-Ran Cai*, Chong-Yang Wang, Xu-Sheng Liu, Ji-Qiang Zhang, Kang Jin, and Wen-Li Yang, Combined effect of simplicial complexes and interlayer interaction: An example of information-epidemic dynamics on multiplex networks, Phys. Rev. Res. 5, 013196 (2023). 

10) Liang Zhang, Chao-Ran Cai*, Ji-Qiang Zhang, Xu-Sheng Liu, Chong-Yang Wang, and Zhi-Xi Wu, Nonlinear mapping between continuous- and discrete-time dynamics, EPL 137, 61002 (2022).

9) Xin Chang, Chao-Ran Cai*, Ji-Qiang Zhang, and Chong-Yang Wang, Analytical solution of epidemic threshold for coupled information-epidemic dynamics on multiplex networks with alterable heterogeneity, Phys. Rev. E 104, 044303 (2021).

8) Xin Chang and Chao-Ran Cai*, Analytical computation of the epidemic prevalence and threshold for the discrete-time susceptible–infected-susceptible dynamics on static networks, Physica A 571, 125850 (2021).

7) Chao-Ran Cai, Zhi-Xi Wu*, and Petter Holme*, Multistage onset of epidemics in heterogeneous networks, Phys. Rev. E 103, 032313 (2021).

6) Chao-Ran Cai* and Zhi-Xi Wu*, Analytical treatment for cyclic three-state dynamics on static networks, Phys. Rev. E 101, 012305 (2020).

5) Guo-Mei Tang, Chao-Ran Cai, and Zhi-Xi Wu*, Evolutionary vaccination dynamics with internal support mechanisms, Physica A 473, 135–143 (2017).

4) Chao-Ran Cai, Zhi-Xi Wu*, Michael Z. Q. Chen, Petter Holme, and Jian-Yue Guan, Solving the Dynamic Correlation Problem of the Susceptible-Infected-Susceptible Model on Networks, Phys. Rev. Lett. 116, 258301 (2016).

3) Chao-Ran Cai, Zhi-Xi Wu*, and Jian-Yue Guan, Effective degree Markov-chain approach for discrete- time epidemic processes on uncorrelated networks, Phys. Rev. E 90, 052803 (2014).

2) Chao-Ran Cai, Zhi-Xi Wu*, and Jian-Yue Guan, Effect of vaccination strategies on the dynamic behavior of epidemic spreading and vaccine coverage, Chaos Solitons Fractals 62-63, 36–43 (2014).

1) Chao-Ran Cai, Zhi-Xi Wu*, and Jian-Yue Guan, Behavior of susceptible- vaccinated– infected– recovered epidemics with diversity in the infection rate of individuals, Phys. Rev. E 88, 062805 (2013).

复杂网络上的动力学，以传播动力学为主。