We study an optoelectronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly stable fixed point, which, when subjected to a finite-amplitude perturbation, loses stability initially via a periodic train of ultrafast pulses. We derive approximate mappings that do an excellent job of capturing the observed instability. The oscillator provides a simple device for fundamental studies of time-delay dynamical systems and can be used as a building block for ultrawide-band sensor networks.
-We study an optoelectronic time-delay oscillator with bandpass filtering for different values of the filter bandwidth. Our experiments show novel pulse-train solutions with pulse widths that can be controlled over a three-order-of-magnitude range, with a minimum pulse width of ∼ 150 ps. The equations governing the dynamics of our optoelectronic oscillator are similar to the FitzHugh-Nagumo model from neurodynamics with delayed feedback in the excitable and oscillatory regimes. Using a nullclines analysis, we derive an analytical proportionality between pulse width and the low-frequency cutoff of the bandpass filter, which is in agreement with experiments and numerical simulations. Furthermore, the nullclines help to describe the shape of the waveforms. Copyright c EPLA, 2011Introduction. -Excitability is an essential characteristic of many biological systems, such as neural networks and the heart [1]. The FitzHugh-Nagumo (FHN) model [2] is a canonical model of excitability, which exhibits a variety of dynamics ranging from spiking to relaxation oscillations. The study of excitability in optics and electronics is of great current interest [3][4][5][6].There is also great interest in developing devices that produce periodic trains of optical pulses, which correspond to distinct comb lines in the frequency domain, for applications ranging from metrology [7] to frequency conversion and signal broadcasting [8]. Narrow pulses, with correspondingly large bandwidths, are particularly useful. Therefore, the ability to tune pulse widths to short time scales is very desirable.In this letter, we describe novel pulse-train solutions generated by a time-delay optoelectronic oscillator (OEO). Using nullclines corresponding to solutions that are periodic with the time delay, we find an analytic expression relating the pulse width to the low-frequency cutoff of the bandpass filter in our system. The analytic expression is in good agreement with experiments and numerical simulations. We also apply a similar analysis to the oscillatory regime, where we can control the duty cycle of the limit-cycle oscillations. Again, the nullclines make analytical studies of the waveforms of these solutions possible.
We demonstrate the control of chaos in a nonlinear circuit constructed from readily available electronic components. Control is achieved using recursive proportional feedback, which is applicable to chaotic dynamics in highly dissipative systems and can be implemented using experimental data in the absence of model equations. The application of recursive proportional feedback to a simple electronic oscillator provides an undergraduate laboratory problem for exploring proportional feedback algorithms used to control chaos.
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