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Neimark–Sacker Bifurcation Analysis and 0–1 Chaos Test of an Interactions Model between Industrial Production and Environmental Quality in a Closed Area

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  • Baogui Xin

    (Nonlinear Science Center, College of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, China)

  • Zhiheng Wu

    (Nonlinear Science Center, College of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, China)

Abstract

A discrete-time model is presented to describe the complex interaction between industrial production and environmental quality in a closed area. Its Neimark–Sacker bifurcation and chaos are discussed based on Wen’s explicit Neimark–Sacker bifurcation criterion, Kuznetsov’s normal form method and center manifold theory and Gottwald and Melbourne’s 0–1 test algorithm. Numerical simulations are employed to validate the main results of this work.

Suggested Citation

  • Baogui Xin & Zhiheng Wu, 2015. "Neimark–Sacker Bifurcation Analysis and 0–1 Chaos Test of an Interactions Model between Industrial Production and Environmental Quality in a Closed Area," Sustainability, MDPI, vol. 7(8), pages 1-19, July.
    • Handle: RePEc:gam:jsusta:v:7:y:2015:i:8:p:10191-10209:d:53474
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    References listed on IDEAS

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    1. Mehdi Aliehyaei & Farideh Atabi & Mohammad Khorshidvand & Marc A. Rosen, 2015. "Exergy, Economic and Environmental Analysis for Simple and Combined Heat and Power IC Engines," Sustainability, MDPI, vol. 7(4), pages 1-14, April.
    2. Xin, Baogui & Ma, Junhai & Gao, Qin, 2009. "The complexity of an investment competition dynamical model with imperfect information in a security market," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2425-2438.
    3. Dorel Paraschiv & Cristiana Tudor & Radu Petrariu, 2015. "The Textile Industry and Sustainable Development: A Holt–Winters Forecasting Investigation for the Eastern European Area," Sustainability, MDPI, vol. 7(2), pages 1-12, January.
    4. Dinda, Soumyananda, 2004. "Environmental Kuznets Curve Hypothesis: A Survey," Ecological Economics, Elsevier, vol. 49(4), pages 431-455, August.
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    Cited by:

    1. Uddin, Md. Jasim & Rana, Sarker Md. Sohel & Işık, Seval & Kangalgil, Figen, 2023. "On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Chen Zhang & Xianyi Li, 2023. "Dynamics of a Discrete Leslie–Gower Model with Harvesting and Holling-II Functional Response," Mathematics, MDPI, vol. 11(15), pages 1-19, July.

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