New 4D and 3D models of chaotic systems developed from the dynamic behavior of nuclear reactors

The complex, highly nonlinear dynamic behavior of nuclear reactors can be captured qualitatively by novel four-dimensional (that is, fourth order) and three-dimensional (that is, third order) models of chaotic systems and analyzed with Lyapunov spectra, bifurcation diagrams, and phase diagrams. The chaotic systems exhibit a rich variety of bifurcation phenomena, including the periodic-doubling route to chaos, reverse bifurcations, anti-monotonicity, and merging chaos. The offset boosting method, which relocates the attractor's basin of attraction in any direction, is demonstrated in these chaotic systems. Both constant parameters and periodic functions are seen in offset boosting phenomena, yielding chaotic attractors with controlled mean values and coexisting attractors.