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In this work, we have proposed electro-optical nonlinear delayed feedback systems (NDFS) using VCSEL. NDFS is composed by non-linear function unit, a transfer function unit, a gain adjusting unit and delay elements unit. In this system, with the increase of the feedback gain, cyclic oscillations from the non-oscillating state arise, and they repeatedly come to be harmonic or bifurcation transitions, leading to chaotic oscillation. With our experiments, we carried out the simulations, to prove the waveform generated from our NDFS to be really chaotic. In addition, we examined the influence of the external input signals to this process. As a result, we proved that random waveforms seen in the experiments to be really chaotic oscillations by comparison to theoretical chaotic feature. Also, we have observed period entrainment by varying external input frequency or delaytime of NDFS when we add sinusoidal wave with appropriate amplitude to LD driving current in the experiment. Moreover we have observed weak entrainment, strong entrainment, and unchanged period or frequency as varying these parameters step by step. Intervals of frequency or delaytime at the very time of occurring entrainment was determined by above mentioned parameters. Thus, we have clarified that intervals of frequency when occurring entrainment corresponds to the reciprocal of the delaytime when we varied frequency so as to stabilize the delaytime. On the other hand, we have also clarified that intervals of delaytime at the occurring entrainment corresponds to the reciprocal of input frequency when we varied delaytime so as to stabilize the frequency. Also, we have measured spectrum with the peak of input frequency as well as integral multiplication of the frequency when entrainments occur. With these results, it is revealed that NDFS in our experiments shows significant characteristics as to vary the waveforms dynamically by external input signal.
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