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Ergodicity and bifurcations for stochastic logistic equation with non-Gaussian Lévy noise

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  • Huang, Zaitang
  • Cao, Junfei

Abstract

In this paper, we will prove that the local RDS φ generated by the stochastic logistic equation with non-Gaussian Lévy noise is continuous, linear and crude cocycle by basing on multiplicative ergodic theorem. Then we determine all invariant measures of the local RDS φ generated by the stochastic logistic equation with non-Gaussian Lévy noise, and we calculate the Lyapunov exponent for each of these measures. Furthermore, we will show that the stochastic logistic equation with non-Gaussian Lévy noise admits a D-bifurcations which is significantly different from the classical Brownian motion process.

Suggested Citation

  • Huang, Zaitang & Cao, Junfei, 2018. "Ergodicity and bifurcations for stochastic logistic equation with non-Gaussian Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 1-10.
    • Handle: RePEc:eee:apmaco:v:330:y:2018:i:c:p:1-10
    DOI: 10.1016/j.amc.2018.01.054
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    Cited by:

    1. Kelty-Stephen, Damian G. & Mangalam, Madhur, 2022. "Fractal and multifractal descriptors restore ergodicity broken by non-Gaussianity in time series," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Huang, Zaitang & Li, Qi & Cao, Junfei, 2021. "Dynamics in a stochastic diffusive plant-herbivore system," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Yang, Yanling & Wang, Qiubao, 2023. "Capture of stochastic P-bifurcation in a delayed mechanical centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Xuege Wang & Fengqin Yan & Yinwei Zeng & Ming Chen & Bin He & Lu Kang & Fenzhen Su, 2021. "Ecosystem Services Changes on Farmland in Response to Urbanization in the Guangdong–Hong Kong–Macao Greater Bay Area of China," Land, MDPI, vol. 10(5), pages 1-16, May.

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