The Analysis of Global Stability Boundary and Multistability in the Nonlinear Dynamical System of an Advanced Heavy Water Reactor

References

• J. MARCH-LEUBA, “Dynamic Behavior of Boiling Water Reactors,” PhD Thesis, University of Tennessee (1984).
   Google Scholar
• RIZWAN-UDDIN, “Turning Points and Sub- and Supercritical Bifurcations in a Simple BWR Model,” Nucl. Eng. Des., 236, 267 (2006); https://doi.org/10.1016/j.nucengdes.2005.08.003.
   Web of Science ®Google Scholar
• J. MARCH-LEUBA, D. G. CACUCI, and R. B. PEREZ, “Nonlinear Dynamics and Stability of Boiling Water Reactors: Part 1—Qualitative Analysis,” Nucl. Sci. Eng., 93, 111 (1986); https://doi.org/10.13182/NSE86-A17663.
   Web of Science ®Google Scholar
• J. MARCH-LEUBA, D. G. CACUCI, and R. B. PEREZ, “Nonlinear Dynamics and Stability of Boiling Water Reactors: Part 2—Qualitative Analysis,” Nucl. Sci. Eng., 93, 124 (1986); https://doi.org/10.13182/NSE86-A17664.
   Web of Science ®Google Scholar
• D. G. CACUCI, “On Chaotic Dynamics in Nuclear Energy Systems,” Nucl. Technol., 103, 303 (1993); https://doi.org/10.13182/NT93-A34853.
   Web of Science ®Google Scholar
• D. G. CACUCI, “Global Optimization and Sensitivity Analysis,” Nucl. Sci. Eng., 104, 78 (1990); https://doi.org/10.13182/NSE90-A23704.
   Web of Science ®Google Scholar
• J. MARCH-LEUBA, D. G. CACUCI, and R. B. PEREZ, “Universality and Aperiodic Behavior of Nuclear Reactors,” Nucl. Sci. Eng., 86, 401 (1984); https://doi.org/10.13182/NSE84-A18640.
   Web of Science ®Google Scholar
• J. MARCH-LEUBA, D. G. CACUCI, and R. B. PEREZ, “Nonlinear Dynamics of Boiling Water Reactors,” Trans. Am. Nucl. Soc., 45, 725 (1983).
   Google Scholar
• J. MARCH-LEUBA, D. G. CACUCI, and R. B. PEREZ, “Calculation of Limit Cycle Amplitudes in Commercial Boiling Water Reactors,” Trans. Am. Nucl. Soc., 46, 749 (1984).
   Google Scholar
• D. G. CACUCI, J. MARCH-LEUBA, and R. B. PEREZ, “Limit Cycles and Bifurcations in Nuclear Systems,” Trans. Am. Nucl. Soc., 53, 239 (1986).
   Google Scholar
• M. TSUJI et al., “Stability Analysis of BWRs Using Bifurcation Theory,” J. Nucl. Sci. Technol., 30, 1107 (1993); https://doi.org/10.1080/18811248.1993.9734596.
   Web of Science ®Google Scholar
• L. J. DER and C. PAN, “Nonlinear Analysis for a Nuclear-Coupled Two-Phase Natural Circulation Loop,” Nucl. Eng. Des., 235, 613 (2005); https://doi.org/10.1016/j.nucengdes.2004.09.008.
   Web of Science ®Google Scholar
• G. V. DURGA PRASAD and M. PANDEY, “Stability Analysis and Nonlinear Dynamics of Natural Circulation Boiling Water Reactors,” Nucl. Eng. Des., 238, 229 (2008); https://doi.org/10.1016/j.nucengdes.2007.05.004.
   Web of Science ®Google Scholar
• A. K. KARVE, “Nuclear-Coupled Thermal Hydraulic Stability Analysis of Boiling Water Reactors” PhD Thesis, University of Virginia (1998).
   Google Scholar
• A. DOKHANE et al., “Spatial and Model-Order Based Reactor Signal Analysis Methodology for BWR Core Stability Evaluation,” Ann. Nucl. Energy, 33, 1329 (2006).
   Web of Science ®Google Scholar
• C. LANGE et al., “Comments on the Application of Bifurcation Analysis in BWR Stability Analysis,” Prog. Nucl. Energy, 68, 1 (2013); https://doi.org/10.1016/j.pnucene.2013.04.003.
   Web of Science ®Google Scholar
• C. LANGE, D. HENNIG, and A. HURTADO, “An Advanced Reduced Order Model for BWR Stability Analysis,” Prog. Nucl. Energy, 53, 139 (2011); https://doi.org/10.1016/j.pnucene.2010.07.006.
   Web of Science ®Google Scholar
• C. LANGE, D. HENNIG, and A. HURTADO, “Remarks to a Novel Nonlinear BWR Stability Analysis Approach (RAM-ROM Methodology),” In Proceeding of Advances in Nuclear Fuel Management IV (ANFM 2009), South Carolina, USA.
   Google Scholar
• C. LANGE et al., “Complex BWR Dynamics from the Bifurcation Theory Point of View,” Ann. Nucl. Energy, 67, 91 (2014); https://doi.org/10.1016/j.anucene.2013.07.034.
   Web of Science ®Google Scholar
• V. PANDEY and S. SINGH, “A Bifurcation Analysis of Boiling Water Reactor on Large Domain of Parametric Spaces,” Commun. Nonlinear Sci. Numer. Simul., 38, 30 (2016); https://doi.org/10.1016/j.cnsns.2016.01.018.
   Web of Science ®Google Scholar
• V. PANDEY and S. SINGH, “Bifurcation Analysis of the Simplified Models of Boiling Water Reactor and Identification of Global Stability Boundary,” Nucl. Eng. Des., 315, 93 (2017); https://doi.org/10.1016/j.nucengdes.2017.01.033.
   Web of Science ®Google Scholar
• P. WAHI and V. KUMAWAT, “Nonlinear Stability Analysis of a Reduced Order Model of Nuclear Reactors: A Parametric Study Relevant to the Advanced Heavy Water Reactor,” Nucl. Eng. Des., 241, 134 (2011); https://doi.org/10.1016/j.nucengdes.2010.11.006.
   Web of Science ®Google Scholar
• V. PANDEY and S. SINGH, “Detailed Bifurcation Analysis with a Simplified Model for Advance Heavy Water Reactor System,” Commun. Nonlinear Sci. Numer. Simul., 20, 186 (2015); https://doi.org/10.1016/j.cnsns.2014.05.019.
   Web of Science ®Google Scholar
• C. LIU, X. LIU, and S. LIU, “Bifurcation Analysis of a Morris-Lecar Neuron Model,” Biol. Cybern., 108, 75 (2014); https://doi.org/10.1007/s00422-013-0580-4.
   PubMed Web of Science ®Google Scholar
• Z. ZHAO, B. JIA, and H. GU, “Bifurcations and Enhancement of Neuronal Firing Induced by Negative Feedback,” Nonlinear Dyn., 86, 1549 (2016); https://doi.org/10.1007/s11071-016-2976-x.
   Web of Science ®Google Scholar
• D. GHOSH, A. R. CHOWDHURY, and P. SAHA, “Bifurcation Continuation, Chaos and Chaos Control in Nonlinear Bloch System,” Commun. Nonlinear Sci. Numer. Simul., 13, 1461 (2008); https://doi.org/10.1016/j.cnsns.2007.03.009.
   Web of Science ®Google Scholar
• W.-S. SON and Y.-J. PARK, “Delayed Feedback on the Dynamical Model of a Financial System,” Chaos, Solitons Fractals, 44, 208 (2011); https://doi.org/10.1016/j.chaos.2011.01.010.
   Web of Science ®Google Scholar
• Y. BI et al., “Bifurcation Analysis and Potential Landscapes of the p53-Mdm2 Module Regulated by the Co-Activator Programmed Cell Death 5,” Chaos, 25 (2015); https://doi.org/10.1063/1.4934967.
   PubMed Web of Science ®Google Scholar
• Y. A. KUZNETSOV, Elements of Applied Bifurcation Theory, 2nd ed., Springer, New York (1998).
   Google Scholar
• R. K. SINHA and A. KAKODKAR, “Design and Development of the AHWR—The Indian Thorium Fuelled Innovative Nuclear Reactor,” Nucl. Eng. Des., 236, 683 (2006); https://doi.org/10.1016/j.nucengdes.2005.09.026.
   Web of Science ®Google Scholar
• A. DHOOGE, W. GOVAERTS, and Y. A. KUZNETSOV, “Matcont: A Matlab Package for Numerical Bifurcation Analysis of ODEs,” ACM Transactions on Mathematical Software, 29, 141, (2003).
   Google Scholar