## Appendix B Mathematical Model  
The model consisted of a point-kinetic approximation of the distribution of neutrons, delayed neutron precursors and a lumped-parameter system of the fuel and coolant temperatures. The model held \(K\) groups of precursors represented by the vector \(\vec{\lambda}\) of decay constants and the vector \(\vec{\beta}\) of delayed neutron fractions. The equation of the reactor core power \(P\) is given by  
\[\frac{\partial P}{\partial t}=\frac{\rho-\beta}{l_{0}}P+\left(\vec{\lambda}, \vec{\zeta}\right), \tag{5}\]  
where \(l_{0}\) is the mean neutron generation time, \(\vec{\zeta}\) is the vector of the precursor's number density times' energy release, \(\beta=(1,\vec{\beta})\) is the total delayed neutron fraction, \(\vec{\lambda}\) is the vector of delayed neutrons decay constant and \(\rho\) is the reactor core reactivity. The last term of the equation represents the delayed neutron source, which is equal to the dot-product of vector \(\vec{\lambda}\) and vector \(\vec{C}\). The equation of the energy release associated with the delayed neutrons is given by  
\[\frac{\partial\vec{C}}{\partial t}=\frac{\vec{\beta}}{l_{0}}P-\mathrm{d} \mathrm{g}\vec{\lambda}\ \ \vec{C}, \tag{10}\]  
where \(\mathrm{d}\mathrm{g}\vec{\lambda}\) stands for a diagonal matrix whose main diagonal is vector \(\vec{\lambda}\). Assuming the reactor core comprises fuel and coolant regions, then the time-dependent fuel temperature \(T_{f}\) and coolant temperature \(T_{c}\) averaged over the corresponding region are described by the lumped-parameter thermal-hydraulic equations. The system of equations for the fuel and coolant temperature change is given by  
\[M_{f}C_{pf}\frac{\partial T_{f}}{\partial t}=P+a_{h}(T_{c}-T_{f}), \tag{11}\]  
\[M_{c}C_{pc}\bigg{(}\frac{\partial T_{c}}{\partial t}+v\frac{T_{c}-T_{in}}{L} \bigg{)}=a_{h}(T_{f}-T_{c}), \tag{12}\]  
where \(M_{i}\) is a mass, \(C_{pi}\) is a specific heat capacity, \(v\) is a flow rate, \(L\) is the length of the channel, \(a_{h}\) is a heat transfer coefficient from the fuel to the coolant regions and \(T_{in}\) is the temperature of the inlet coolant flow. The reactivity \(\rho\) is a function of the coolant and fuel temperatures due to the Doppler and coolant density effects. In this study, we assumed the reactivity was a linear function near a steady-state temperatures of the fuel \(T_{f}^{0}\) and the coolant \(T_{c}^{0}\), that is,  
\[\rho=\rho_{0}+\alpha_{D}(T_{f}-T_{f}^{0})+\alpha_{c}(T_{c}-T_{c}^{0}), \tag{13}\]  
where \(\rho_{0}\) stands for the external reactivity insertion by means of control rods, \(\alpha_{D}\) stands for the Doppler reactivity coefficient and \(\alpha_{c}\) stands for the total reactivity coefficient of the coolant temperature and density. The model has two steady-states \(M_{0}\) and \(M_{1}\), which correspond to zero power and to zero reactivity. The former trivial state \(M_{0}\) given by  
\[M_{0}:\ P=0,\ \ \vec{C}=0,\ T_{f}=T_{in},\ T_{c}=T_{in}, \tag{14}\]  
remains stable while the total reactivity \(\rho<0\). The zero-reactivity state \(M_{1}\) is given by  
\[M_{1}:\ P=P_{0},\ \ \vec{C}=\frac{\vec{\beta}}{l_{0}}P_{0},\ T_{f}=T_{c}+\frac{ P_{0}}{a_{h}},\ T_{c}=T_{in}+\frac{P_{0}}{M_{c}C_{pc}}\frac{L}{v}, \tag{15}\]  
where the steady-state power \(P_{0}\) is determined by the equation \(\rho=0\). In our simulations, the model transient always started from the zero-reactivity state \(M_{1}\). The specific parameters of the model corresponded to a pressurized water reactor (PWR) core. The total fraction \(\beta\) of delayed neutrons was equal to 700 pcm. The lumped parameters of the fuel and coolant thermal-hydraulic model are presented in Table 10. The parameters of the six group emitters are presented in Table 10.  
The model simulated the transients initiated by a positive reactivity introduced at the HZP and HFP reactor core states. The excessive reactivity was injected gradually from 0 to 10 ms and then remained unchanged.