My research lies in applied dynamical systems and the analysis of high-dimensional nonlinear models. I study how structured perturbations alter qualitative behavior, with emphasis on transitions between dynamical regimes in systems exhibiting nonlinear or chaotic dynamics, often through the lens of neuroscience.
I investigate these transitions through a combination of numerical simulation and parameter exploration, using computation as a tool to probe bifurcation structure, stability, and emergent dynamics. Although the applications are largely in neural circuits, the approach is always mathematical: understanding how nonlinear structure organizes behavior in dynamical systems.
Parkinson's Disease Modeling
Loss of dopamine within the basal ganglia (BG) leads to neuronal activity changes, including altered firing rates and firing patterns, thought to underlie parkinsonian motor symptoms. Yet, within BG neuronal populations, baseline activity and responses to inputs are highly variable, complicating efforts to identify key factors associated with pathological changes.
I develop a novel approach to constructing heterogeneous biophysical computational neural models that statistically agrees with diverse firing properties observed across slice and in vivo recordings of the substantia nigra pars reticulata (SNr) in healthy and diseased rodents. The model reproduces diverse responses to GABAergic stimulation and enables systematic exploration of parameter perturbations to identify mechanisms for diseased network dynamics and responses to stimulation.
Chaotic Dynamics and Control in Neural Systems
Nonlinear dynamical systems often exhibit rich qualitative behavior, including chaos, where trajectories evolve on strange attractors with sensitive dependence on initial conditions. This research develops a framework to control that chaotic neural behavior through perturbations that take advantage of the structure of the strange attractor. Binary control sequences are applied at prescribed intersections with Poincare sections that stabilize unstable periodic orbits, resulting in structures called cupolets (chaotic unstable periodic orbit-lets).
Extending this work to networks of coupled oscillators, we find how local control signals propagate through graph structures and how coupling reshapes the global stability landscape. Current directions include characterizing when distinct sequences generate homologous periodic orbits and how attractor geometry constrains admissible control sequences.
Scientific Software and Computational Methods
This research direction focuses on the development of computational frameworks for systematic analysis and classification of dynamical behavior in neural models and experimental data. The STReaC (Spike Train Response and Classification) toolbox provides an open-source reproducible Python pipeline for comparing spike train responses to a reference period for enhanced classification of response types.
Recent work has focused on developing supervised classification of neural spike trains as either being healthy or diseased (Parkinsonian). This classifier has been used to measure the performance of novel intervention for motor rescue in rodents. Additionally, current work is developing a library for improved burst-detection through integration of multiple algorithms. These tools enable open-source, robust, and reproducible feature extraction of neural spike trains.