On Chaotic Dynamics in Nuclear Engineering Systems

The mapping ρ_n+1 = φ[ρ_n + kQ₀(exp ρ_n — 1)] is shown to belong to the universal class of quadratic mappings with a negative Schwarzian derivative, thus rigorously providing the reasons underlying this mapping’s ability to follow the well-known Feigenbaum scenario to deterministic chaos. This scenario proceeds through an infinite cascade of period-doubling bifurcations, as noted in numerical experiments by Shabalin in a recent paper on power instabilities in periodically pulsed reactors. An analysis of this paper is also presented together with an overall perspective of the current state of research on chaotic dynamics in nuclear engineering systems.