Abstract: During the cold start-up, the reactor is in sub-critical state. Therefore, the external neutron source cannot be neglected. In this research paper, the analytical solution of neutron point kinetics equations with a group of delayed neutrons in the presence of the pulsed neutron source in a pressurized-water reactor with ²³⁵U as a fuel is presented. The analytical solution is based on the expansion of the neutron density in powers of the prompt neutrons generation time. The point kinetics equations with this method are solvable for step and ramp reactivity and lead to better results compared with other analytical works, but are not solvable for sinusoidal reactivity. So, the neutron density response to sinusoidal reactivity is analyzed by using the fixed point and Lyapunov exponents method.

Keywords: Pulsed neutron source, Prompt neutrons generation time, Lyapunov exponent, Neutron density
J. of Nucl Sci. and Tech 71