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Stability and Hopf bifurcation analysis for an energy resource system

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Abstract

This paper investigates the dynamical behaviors for a four-dimensional energy resource system with time delay, especially in terms of equilibria analyses and Hopf bifurcation analysis. By setting the time delay as a bifurcation parameter, it is shown that Hopf bifurcation would occur when the time delay exceeds a sequence of critical values. Furthermore, the stability and direction of the Hopf bifurcation are determined via the normal form theory and the center manifold reduction theorem. Numerical examples are given in the end of the paper to verify the theoretical results.

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Acknowledgments

This work was jointly supported by the State Grid Corporation of China (DZN1720130019), the National Natural Science Foundation of China under grant 61272530 and 11072059, the Natural Science Foundation of Jiangsu Province of China under Grant BK2012741, and the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20110092110017 and 20130092110017. The authors would like to give thanks to the anonymous reviewers and the handling editor for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Automation, Southeast University, Nanjing , 210096, China

    Jianqiang Hu

  2. China Electric Power Research Institute, Nanjing , 210003, China

    Jianqiang Hu

  3. Research Center for Complex Systems and Network Sciences, and Department of Mathematics, Southeast University, Nanjing , 210096, China

    Jinde Cao

  4. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah , 21589, Saudi Arabia

    Jinde Cao & Tasawar Hayat

  5. Department of Mathematics, Quaid-I-Azam University, Islamabad , 44000, Pakistan

    Tasawar Hayat

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  1. Jianqiang Hu
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  2. Jinde Cao
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  3. Tasawar Hayat
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Correspondence to Jinde Cao.

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Hu, J., Cao, J. & Hayat, T. Stability and Hopf bifurcation analysis for an energy resource system. Nonlinear Dyn 78, 219–234 (2014). https://doi.org/10.1007/s11071-014-1434-x

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  • DOI: https://doi.org/10.1007/s11071-014-1434-x

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