Stability analysis in nuclear reactor using Lyapunov exponent

A novel approach for the potential parameters selection of Peyrard–Bishop model

“…By the year 1999, Hiroshi Shibata introduced mean Lyapunov exponent (MLE) in order to characterize the chaos of the systems described by PDEs [19]. The MLE theory has attracted researchers attention and has improved its applications in several fields [20][21][22][23][24] Letter, we have used this theory to select the potential parameters of the PB model. Theoretical analysis indicates that the best range for potential parameters is where the MLE is at its smaller values, which means that spatial pattern of this system is ordered [19].…”

Analyzing stability of neutron point kinetics equations with nine photo-neutron groups using Lyapunov exponent method

“…Recently, Della et al [13] has developed a theoretical model to study the stability of Ghana Research Reactor (GHARR-1) for a single group of delayed neutrons taking into consideration thermal hydraulics. Another important method for analyzing and diagnosing instability of nuclear reactors is the spectrum of Lyapunov exponents method, that is based on eigenvalues and eigenvectors of the Jacobian matrix [16][17][18]. The purpose of the research reported here is to introduce the Mean Lyapunov Exponent (MLE 1 ) approach on stability analysis of Neutron Point Kinetic (NPK 2 ) equations in nuclear reactors with six delayed neutron groups and nine photo-neutron groups in the presence of step, ramp and sinusoidal reactivities.…”