My research lies at the interface of control theory, dynamical systems, mathematical neuroscience, and mathematical psychology. I study how to:

○ design control strategies for nonlinear and nonlocal dynamical systems;

○ develop controllability Gramians and synthesis methods beyond the classical linear setting for control-affine systems;

○ build mechanistic models of brain activity and perception, from neural field equations for visual illusions to whole-brain models derived from fMRI or EEG.

I am particularly interested in energy-efficient control and trajectory-dependent notions of controllability for large-scale network and field models.

Control theory · Nonlinear and nonlocal dynamical systems · Neural field equations · Whole-brain modeling · Network neuroscience · Mathematical psychology · Sub-Riemannian geometry and degenerate PDEs.

I have focused on the mathematical modeling of MacKay-type visual illusions in the field of neuroscience and psychology. Specifically, my research has explored the visual MacKay effect and Billock and Tsou’s visual illusions. By controlling a one-layer Amari-type neural field equation, we have sought to uncover the underlying neural mechanisms of these intriguing visual phenomena.

More precisely, via mathematical modeling, analysis, and computations, my work has explored how the intrinsic circuitry of the primary visual cortex (V1) generates the patterns of activity underlying:

○ the visual MacKay effect (from redundant stimulation), and

○ the psychophysical experiments reported by Billock and Tsou (funnel patterns in foveal or peripheral vision).

To this end, we proposed a controllability-based approach for a one-layer Amari-type neural field equation that models the average membrane potential of V1 neurons, including sensory inputs from the retina. We then proved qualitative concordance between the model’s output patterns and observed perceptual responses. Selected works are hal.science, and hal.science.