Lyapunov exponent method is one of the best tools for investigating the range of stability and the transient behavior of the dynamical systems. In beryllium-moderated and heavy water-moderated reactors, photo-neutron plays an important role in dynamic behavior of the reactor. Therefore, stability analysis for changes in the control parameters of the reactor in order to guarantee safety and control nuclear reactor is important. In this work, the range of stability has been investigated using Lyapunov exponent method in response to step, ramp and sinusoidal external reactivities regarding six groups of delayed neutrons plus nine groups of photo-neutrons. The qualitative results are in good agreement with quantitative results of other works


1. A N Abdallah, Nuc. Eng. Des. 238 (2008) 2648.
2. E A Ahmed, Nucl. Eng. Des. 224 (2003) 279.
3. D L Hetrick, “Dynamics of Nuclear Reactors”, American Nuclear Society, La Grange Park (1993).
4. G R Keepin, “Physics of Nuclear Kinetics”, Addison-Wesley Publishing Company, Inc., Massachusetts (1965).
5. E W Lynn, “Reactor Dynamics and Control”, American Elsevier Publishing Company, INC., New York (1968).
6. F Jatuff, A L Thi, M Murphy, T Williams, and R Chawla, Ann. Nucl. Energy 30 (2003) 1731.
7. A N Abdallah, Nucl. Eng. Des. 240 (2010) 1622.
8. F Y Li, Z Chen, and Y Liu, Prog. Nucl. Energy 67 (2013) 15.
9. L Z Fu, “Nuclear Reactor Kinetics”, Atomic Energy Press, Beijing (1988).
10. J D Lewins and E N Ngcobo, Ann. Nucl. Energy 23 (1996) 29.
11. J L Munoz-Cobo, C Garca, A Escriva, and J Melara, Ann. Nucl. Energy 35 (2008) 1185.
12. A Hainoun, I Khamis, and G Saba, Nucl. Eng. Des. 232 (2004) 19.
13. R Della, E Alhassan, N A Adoo, C Y Bansah, B J B Nyarko, and E H K Akaho, Energy Convers Manage 74 (2013) 587.
14. W Z Chen, B Kuang, and L F Guo, Nucl. Eng. Des. 236 (2006) 1326.
15. W K Ergen, H J Lipkin, and J A Nohel, Journal of Mathematics and Physics 36 (1957) 36.
16. T Suzudo, Prog. Nucl. Energy 43 (2003) 217.
17. R Khodabakhsh, S Behnia, and O Jahanbakhsh, Ann. Nucl. Energy 35 (2008) 1370.
18. M Shayesteh, S Behnia, and A Abdi Saray, Ann. of Nucl. Energy 43 (2012) 131.
19. S Glasstone and A Sesonske, “Nuclear Reactor Engineering”, Chapman & Hall Inc. (1981).
20. A Hainoun and I Khamis, Nucl. Eng. Des. 195 (2000) 299.
21. K Almenas and R Lee, “Nuclear Engineering an Introduction”, Springer, Berlin (1992).
22. T Sathiyasheela, Ann. of Nucl. Energy 36 (2009) 246.
23. J J Duderstadt and L J Hamilton, “Nuclear Reactor Analysis”, John Wiley and Sons, USA (1976).
24. W M Stacey, “Nuclear Reactor Physics”, John Wiley and Sons, Inc., USA, (2001).
25. E Ott, “Chaos in dynamical system”, Cambridge University Press, Canada (1993).
26. B J West, A L Goldberger, G Rouner, and V Bhar-gava, Physica D 17 (1985) 198.
27. A Wolf, J B Swift, H L Swinney, and J A Vastano, Physica D 16 (1985) 285.
28. R Hilborn, “Chaos and nonlinear dynamics”, Oxford University Press (2000).
29. J R Dorfman, “An Introduction to Chaos in Non-Equilibrium Statistical Mechanics”, Cambridge University Press, Cambridge (1999).

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