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Abstract
Characteristic features of a dynamical system are well represented by a Lyapunov exponents map in parametric space. We used this tool to investigate the system governing second-harmonic generation of light with a pulsating external field (square wave). The influence of the pulse parameters on dynamics of the generation process is numerically investigated. Chaotic and hyperchaotic behaviour in the system with a weak damping is found. Bifurcation diagrams as well as some phase portraits are also studied. The interesting case of the short-pulse dynamics and the quasiperiodic behaviour of the system is considered.