We examine the use of synchronization as a mechanism for extracting parameter
and state information from experimental systems. We focus on important aspects
of this problem that have received little attention previously, and we explore
them using experiments and simulations with the chaotic Colpitts oscillator as
an example system. We explore the impact of model imperfection on the ability
to extract valid information from an experimental system. We compare two
optimization methods: an initial value method and a constrained method. Each of
these involve coupling the model equations to the experimental data in order to
regularize the chaotic motions on the synchronization manifold. We explore both
time dependent and time independent coupling. We also examine both optimized
and fixed (or manually adjusted) coupling. For the case of an optimized time
dependent coupling function u(t) we find a robust structure which includes
sharp peaks and intervals where it is zero. This structure shows a strong
correlation with the location in phase space and appears to depend on noise,
imperfections of the model, and the Lyapunov direction vectors. Comparison of
this result with that obtained using simulated data may provide one measure of
model imperfection. The constrained method with time dependent coupling appears
to have benefits in synchronizing long datasets with minimal impact, while the
initial value method with time independent coupling tends to be substantially
faster, more flexible and easier to use. We also describe a new method of
coupling which is useful for sparse experimental data sets. Our use of the
Colpitts oscillator allows us to explore in detail the case of a system with
one positive Lyapunov exponent. The methods we explored are easily extended to
driven systems such as neurons with time dependent injected current.

本研究通过实验和仿真探讨了使用同步作为从实验系统中提取参数和状态信息的机制，探讨了此问题的关键方面，并比较了两种优化方法（初始值法和约束法），发现有时具有时间相关耦合函数 u (t) 的约束方法具有优势，而有时具有时间无关耦合的初始值法更为快速，灵活且易于使用。