bifurcation

Yan, Dingding, He, Mengqi, Cheke, Robert ORCID: https://orcid.org/0000-0002-7437-1934, Zhang, Qianqian and Tang, Sanyi (2024) A stochastic hormesis Ricker model and its application to multiple fields. Chaos, Solitons and Fractals, 185:115131. pp. 1-13. ISSN 0960-0779 (Print), 1873-2887 (Online) (doi:10.1016/j.chaos.2024.115131)

blurred orbit

Yan, Dingding, He, Mengqi, Cheke, Robert ORCID: https://orcid.org/0000-0002-7437-1934, Zhang, Qianqian and Tang, Sanyi (2024) A stochastic hormesis Ricker model and its application to multiple fields. Chaos, Solitons and Fractals, 185:115131. pp. 1-13. ISSN 0960-0779 (Print), 1873-2887 (Online) (doi:10.1016/j.chaos.2024.115131)

change point

He, Sha, Yan, Dingding, Shu, Hongying, Tang, Sanyi, Wang, Xia and Cheke, Robert ORCID: https://orcid.org/0000-0002-7437-1934 (2023) Randomness accelerates the dynamic clearing process of the COVID-19 outbreaks in China. Mathematical Biosciences, 363:109055. ISSN 0025-5564 (Print), 1879-3134 (Online) (doi:10.1016/j.mbs.2023.109055)

data fitting

He, Sha, Yan, Dingding, Shu, Hongying, Tang, Sanyi, Wang, Xia and Cheke, Robert ORCID: https://orcid.org/0000-0002-7437-1934 (2023) Randomness accelerates the dynamic clearing process of the COVID-19 outbreaks in China. Mathematical Biosciences, 363:109055. ISSN 0025-5564 (Print), 1879-3134 (Online) (doi:10.1016/j.mbs.2023.109055)

dose–response curve

Tang, Sanyi, Feng, Xin, Yan, Dingding, Liang, Juhua, Liu, Lili, Xiao, Yanni, Tang, Biao and Cheke, Robert Alexander ORCID: https://orcid.org/0000-0002-7437-1934 (2025) Hormesis and hydra effects revealed by intraspecific overcompensation models and dose–response curves. Journal of the Royal Society Interface, 22 (225). pp. 1-16. ISSN 1742-5689 (Print), 1742-5662 (Online) (doi:10.1098/rsif.2025.0169)

hormesis

Tang, Sanyi, Feng, Xin, Yan, Dingding, Liang, Juhua, Liu, Lili, Xiao, Yanni, Tang, Biao and Cheke, Robert Alexander ORCID: https://orcid.org/0000-0002-7437-1934 (2025) Hormesis and hydra effects revealed by intraspecific overcompensation models and dose–response curves. Journal of the Royal Society Interface, 22 (225). pp. 1-16. ISSN 1742-5689 (Print), 1742-5662 (Online) (doi:10.1098/rsif.2025.0169)

hormetic zone

Yan, Dingding, He, Mengqi, Cheke, Robert ORCID: https://orcid.org/0000-0002-7437-1934, Zhang, Qianqian and Tang, Sanyi (2024) A stochastic hormesis Ricker model and its application to multiple fields. Chaos, Solitons and Fractals, 185:115131. pp. 1-13. ISSN 0960-0779 (Print), 1873-2887 (Online) (doi:10.1016/j.chaos.2024.115131)

hydra

Tang, Sanyi, Feng, Xin, Yan, Dingding, Liang, Juhua, Liu, Lili, Xiao, Yanni, Tang, Biao and Cheke, Robert Alexander ORCID: https://orcid.org/0000-0002-7437-1934 (2025) Hormesis and hydra effects revealed by intraspecific overcompensation models and dose–response curves. Journal of the Royal Society Interface, 22 (225). pp. 1-16. ISSN 1742-5689 (Print), 1742-5662 (Online) (doi:10.1098/rsif.2025.0169)

mathematical model

Tang, Sanyi, Feng, Xin, Yan, Dingding, Liang, Juhua, Liu, Lili, Xiao, Yanni, Tang, Biao and Cheke, Robert Alexander ORCID: https://orcid.org/0000-0002-7437-1934 (2025) Hormesis and hydra effects revealed by intraspecific overcompensation models and dose–response curves. Journal of the Royal Society Interface, 22 (225). pp. 1-16. ISSN 1742-5689 (Print), 1742-5662 (Online) (doi:10.1098/rsif.2025.0169)

mean first passage time

He, Sha, Yan, Dingding, Shu, Hongying, Tang, Sanyi, Wang, Xia and Cheke, Robert ORCID: https://orcid.org/0000-0002-7437-1934 (2023) Randomness accelerates the dynamic clearing process of the COVID-19 outbreaks in China. Mathematical Biosciences, 363:109055. ISSN 0025-5564 (Print), 1879-3134 (Online) (doi:10.1016/j.mbs.2023.109055)

newly reported cases

He, Sha, Yan, Dingding, Shu, Hongying, Tang, Sanyi, Wang, Xia and Cheke, Robert ORCID: https://orcid.org/0000-0002-7437-1934 (2023) Randomness accelerates the dynamic clearing process of the COVID-19 outbreaks in China. Mathematical Biosciences, 363:109055. ISSN 0025-5564 (Print), 1879-3134 (Online) (doi:10.1016/j.mbs.2023.109055)

overcompensation

Tang, Sanyi, Feng, Xin, Yan, Dingding, Liang, Juhua, Liu, Lili, Xiao, Yanni, Tang, Biao and Cheke, Robert Alexander ORCID: https://orcid.org/0000-0002-7437-1934 (2025) Hormesis and hydra effects revealed by intraspecific overcompensation models and dose–response curves. Journal of the Royal Society Interface, 22 (225). pp. 1-16. ISSN 1742-5689 (Print), 1742-5662 (Online) (doi:10.1098/rsif.2025.0169)

random perturbations

Yan, Dingding, He, Mengqi, Cheke, Robert ORCID: https://orcid.org/0000-0002-7437-1934, Zhang, Qianqian and Tang, Sanyi (2024) A stochastic hormesis Ricker model and its application to multiple fields. Chaos, Solitons and Fractals, 185:115131. pp. 1-13. ISSN 0960-0779 (Print), 1873-2887 (Online) (doi:10.1016/j.chaos.2024.115131)

ricker model

Yan, Dingding, He, Mengqi, Cheke, Robert ORCID: https://orcid.org/0000-0002-7437-1934, Zhang, Qianqian and Tang, Sanyi (2024) A stochastic hormesis Ricker model and its application to multiple fields. Chaos, Solitons and Fractals, 185:115131. pp. 1-13. ISSN 0960-0779 (Print), 1873-2887 (Online) (doi:10.1016/j.chaos.2024.115131)

stochastic difference model

He, Sha, Yan, Dingding, Shu, Hongying, Tang, Sanyi, Wang, Xia and Cheke, Robert ORCID: https://orcid.org/0000-0002-7437-1934 (2023) Randomness accelerates the dynamic clearing process of the COVID-19 outbreaks in China. Mathematical Biosciences, 363:109055. ISSN 0025-5564 (Print), 1879-3134 (Online) (doi:10.1016/j.mbs.2023.109055)