This dissertation expands on existing work to develop a dynamical state and parameter estimation methodology in non-linear systems. The field of parameter and state estimation, also known as inverse problem theory, is a mature discipline concerned with determining unmeasured states and parameters in experimental systems. This is important since measurement of some of the parameters and states may not be possible, yet knowledge of these unmeasured quantities is necessary for predictions of the future state of the system. This field has importance across a broad range of scientific disciplines, including geosciences, biosciences, nanoscience, and many others.

The work presented here describes a state and parameter estimation method that relies on the idea of synchronization of nonlinear systems to control the conditional Lyapunov exponents of the model system. This method is generalized to address any dynamic system that can be described by a set of ordinary first-order differential equations. The Python programming language is used to develop scripts that take a simple text-file representation of the model vector field and output correctly formatted files for use with readily available optimization software.

With the use of these Python scripts, examples of the dynamic state and parameter estimation method are shown for a range of neurobiological models, ranging from simple to highly complicated, using simulated data. In this way, the strengths and weaknesses of this methodology are explored, in order to expand the applicability to complex experimental systems.