Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA.
Philos Trans A Math Phys Eng Sci. 2010 Jan 28;368(1911):343-66. doi: 10.1098/rsta.2009.0225.
We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electro-optic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized, even when the coupling between them is changing unpredictably.
我们描述了一种灵活的模块化延迟反馈非线性振荡器，它能够产生广泛的动力学行为，从周期性振荡到高维混沌。该振荡器使用电光调制和光纤传输，并通过实时数字信号处理实现反馈和滤波。我们考虑了两个相互耦合的这样的振荡器，并确定了它们将同步的条件。通过检查两个耦合振荡器之间的发散或收敛速度，我们量化了系统的最大 Lyapunov 指数或横向 Lyapunov 指数，并提出了一种实验方法来确定这些不需要系统数学模型的速度。最后，我们展示了一种新的自适应控制方法，即使在它们之间的耦合不可预测地变化时，也能保持两个振荡器的同步。
