My research is mainly about exploring complex dynamics involving multiple time scales, particularly bursting, in the neuronal systems, using tools from dynamical systems including geometric singular perturbation theory.
Applications of geometric singular perturbation theory to analyze dynamical systems with two time scales are ubiquitous and well developed. However, there have been fewer reported studies that analyze dynamics involving evolution on three distinct time scales. It is natural to expect that some dynamic phenomena cannot be captured by a two time scale decomposition. One example is the mixed burst mode recorded from subthalamic nucleus (STN) neurons when studying Parkinsonism in rat and primates. This mode consists of long bursts, separated by sequences of short bursts. Such pattern was also observed in recordings and models from respiratory CPG neuron and some models can be very complicated.
Motivated by these models, I am interested in understanding the rhythmic dynamics in multiple time scale systems by using geometric singular perturbation theory and bifurcation analysis. The primary applications have been to bursting dynamics in respiratory neuron models.
Applications of geometric singular perturbation theory to analyze dynamical systems with two time scales are ubiquitous and well developed. However, there have been fewer reported studies that analyze dynamics involving evolution on three distinct time scales. It is natural to expect that some dynamic phenomena cannot be captured by a two time scale decomposition. One example is the mixed burst mode recorded from subthalamic nucleus (STN) neurons when studying Parkinsonism in rat and primates. This mode consists of long bursts, separated by sequences of short bursts. Such pattern was also observed in recordings and models from respiratory CPG neuron and some models can be very complicated.
Motivated by these models, I am interested in understanding the rhythmic dynamics in multiple time scale systems by using geometric singular perturbation theory and bifurcation analysis. The primary applications have been to bursting dynamics in respiratory neuron models.