Extensive theoretical results for the temperature dependence of the static and dynamical structure of undercooled alkali metals using Na and Cs as examples are presented. The static structural properties are obtained from the HMSA integral equations using pair potentials derived from an accurate non-local pscudopotential. The dynamical properties obtained from viscoelastic theory are compared with experiments and the results of memory function formalism. The study indicates that collective density excitations are more dominant in the undercooled region than at their melting points, and that the dynamical properties of Na and Cs exhibit subtle differences in their gross features.

Synchronization behaviour of two mutually coupled double-well Duffig oscillators exhibiting cross-well chaos is examined. Synchronization of the subsystems was observed for coupling strength $k > 0.4$. It is found that when the oscillators are operated in the regime for which two attractors coexist in phase space, basin bifurcation sequences occur leading to $n + 1$, $n \geq 2$ basins as the coupling is varied – a signature of Wada structure and final-state sensitivity. However, in the region of complete synchronization, the basins structure is identical with that of the single oscillators and retains its essential features including fractal basin boundaries.

In this paper, we study the synchronization behaviour of two linearly coupled parametrically excited chaotic pendula. The stability of the synchronized state is examined using Lyapunov stability theory and linear matrix inequality (LMI); and some sufficient criteria for global asymptotic synchronization are derived from which an estimated critical coupling is determined. Numerical solutions are presented to verify the theoretical analysis. We also examined the transition to stable synchronous state and show that this corresponds to a boundary crisis of the chaotic attractor.