YangyangWang - Research

My research lies in dynamical systems and mathematical neuroscience, with a focus on understanding neural activity in central pattern generators (CPGs) that generate rhythmic movements, modulation of neural networks, and sensory feedback control in complex adaptive biological systems, using a variety of mathematical ideas including

dynamical systems theory, geometric singular perturbation theory, and bifurcation theory
mathematical modeling and numerical simulations

Many biological phenomena are governed by complex networks. My work also investigates how network structure influences system dynamics, bifurcations, and function using tools from singularity theory and combinatorial matrix theory.

Mixed-mode oscillations in cortical theta oscillator model and in vitro (Pittman-Polletta et al 2021)

Different types of activity patterns in an embryonic respiratory neuron model (Wang and Rubin 2020)

Multiple-timescale dynamics

An important feature of most biological rhythms is that they evolve on different timescales. I'm particularly interested in modeling and analyzing multiple-timescale activity patterns in neuronal systems. To this end, we have extended the standard fast-slow decomposition method/geometric singular perturbation theory to three or more timescale settings. Applications of interest include uncovering mechanisms underlying non-standard respiratory output patterns and mixed-mode (bursting) oscillations in cortical oscillators.

Publications:

C. Wei, Y. Wang and X. Zhu, Robust Parameter and State Estimation in Multiscale Neuronal Systems Using Physics-Informed Neural Networks, Submitted, 2026. https://arxiv.org/abs/2603.08742
N.A. Phan and Y. Wang, Mixed-Mode Oscillations in a Three-Timescale Coupled Morris-Lecar System, Chaos: An Interdisciplinary Journal of Nonlinear Science, 34, no. 5, 2024
B. Pittman-Polletta, Y. Wang, D. Stanley, C. Schroeder, M. Whittington, N. Kopell, Differential contributions of synaptic and intrinsic inhibitory currents to parsing via flexible phase-locking in neural oscillators, PLoS Computational Biology, 17(4), e1008783, 2021
Y. Wang and J. Rubin, Complex bursting dynamics in an embryonic respiratory neuron model, Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(4), 043127, 2020.
Y. Wang and J. Rubin, Timescales and Mechanisms of Sigh-like Bursting and Spiking in Models of Rhythmic Respiratory Neurons, Journal of Mathematical Neuroscience, 7(1): 3, 2017.
Y. Wang and J. Rubin, Multiple Time Scale Mixed Bursting Dynamics in a Respiratory Neuron Model, Journal of Computational Neuroscience, 41(3), 245-268, 2016.
P. Nan, Y. Wang, V. Kirk, J. Rubin, Understanding and Distinguishing Three-Time-Scale Oscillations: Case Study in a Coupled Morris--Lecar System, SIAM Journal on Applied Dynamical Systems, 14:3, 1518-1557, 2015.

Modulation of neural networks

Breathing is a critical rhythmic behavior that continues from birth up until death. The neural networks that drive breathing are constantly modulated by numerous neuromodulators through altering properties of neurons, synapses and networks. Understanding action of neuromodulation on respiratory networks is critical to understanding neural control of breathing and disorders such as opiod-induced respiratory depression. I have been working closely with experimental collaborators to develop a framework that integrates computational modeling, machine learning, and experimental approaches to examine the modulatory actions that affect respiratory neural control.

Publications:

A.K. Tryba, JC Viemari, Y. Wang and A.J. Garcia III, Noradrenergic neuromodulation produces a NMDAR-dependent network state of respiratory rhythmogenesis in the preBötzinger Complex, Submitted, 2026. https://www.biorxiv.org/content/10.64898/2026.02.11.705209v1
C. Wei, Y. Wang and X. Zhu, Robust Parameter and State Estimation in Multiscale Neuronal Systems Using Physics-Informed Neural Networks, Submitted, 2026. https://arxiv.org/abs/2603.08742
S. Venkatakrishnan, A.K. Tryba, A.J. Garcia III and Y. Wang, Dual mechanisms for heterogeneous responses of inspiratory neurons to noradrenergic modulation, SIAM Journal on Life Sciences, 1(1), 58-98, 2026

Isochrons for a limit cycle with hard boundaries (Wang et al 2021a)

Motor control in sea slug feeding

Motor systems show an overall robustness, but because they are highly nonlinear, understanding how they achieve robustness due to their different components such as sensory feedback and biomechanics is difficult. Through collaboration with experimentalists and theoreticians, we aim to dissect motor robustness against external perturbations, a key but challenging question in motor control.

As a concrete example, we focus on a neuromechanical model of rhythmic feeding behaviors of the marine mollusk, Aplysia californica. This project has also motivated us to develop new methods for studying motor robustness such as infinitesimal shape response curve and local timing response curve, as well as extend classic infinitesimal phase response curve to systems operating within hard limits.

Publications:

Z. Yu, Y. Wang, P.J. Thomas and H.J. Chiel, Tradeoffs in the Energetic Value of Neuromodulation in a Closed-Loop Neuromechanical System, Journal of Theoretical Biology, 604, 112050, 2025
Y. Wang, J.P. Gill, H.J. Chiel and P.J. Thomas, Variational and phase response analysis for limit cycles with hard boundaries, with applications to neuromechanical control problems, Biological Cybernetics, 116, 687–710, 2022
Y. Wang, J.P. Gill, H.J. Chiel and P.J. Thomas, Shape versus timing: linear responses of a limit cycle with hard boundaries under instantaneous and static perturbation, SIAM Journal on Applied Dynamical Systems, 20(2), 701--744, 2021
M.N. Fitzpatrick, Y. Wang, P.J. Thomas, R.D. Quinn, N.S. Szczecinski, Robotics application of a method for analytically computing infinitesimal phase response curves, Conference on Biomimetic and Biohybrid Systems, 104-115, 2020

Hopf/Hopf mode interaction induced by feedforward structure between critical components C1 and C2 (Gandhi et al 2020)

Network structure and dynamics

Networks of coupled dynamical systems arise in many branches of science. In many examples, the network structure influences the dynamics and bifurcations that can be expected to occur generically. We use singularity theory to study how the network structure influences the dynamics and bifurcations in fully inhomogeneous networks, without knowing the specific model equations for each node.

We also study homeostasis, an important biological phenomenon whereby the output of a system (say, body temperature) is approximately constant despite changes of an input (say, ambient temperature). We use singularity theory and combinatorial matrix theory to characterize homeostatic mechanisms in terms of network topology. Based on this theoretical framework, we develop an algorithm that automatically identifies all subnetwork motifs capable of supporting homeostasis using only network structure.

At the other extreme, we study symmetrically coupled identical oscillators and symmetry breaking in such network systems.

Publications:

X. Lin, F. Antoneli and Y. Wang, Automated Classification of Homeostasis Structure in Input-Output Networks, Submitted, 2026. https://arxiv.org/abs/2603.08882
H. Mofidi and Y. Wang, Studying synchronization of neural oscillators through NMDA--AMPA receptor interactions, Chaos, Solitons & Fractals, 202, 117479, 2026
P. Gandhi and Y. Wang, A conceptual framework for modeling a latching mechanism for cell cycle regulation, Mathematical Biosciences, 109396, 2025
Y. Wang, Z. Huang, F. Antoneli and M. Golubitsky, The Structure of Infinitesimal Homeostasis in Input-Output Networks, Journal of Mathematical Biology, 82(7), 1--43. 2021
M. Golubitsky and I. Stewart and F. Antoneli and Z. Huang and Y. Wang, Input-Output Networks, Singularity Theory, and Homeostasis, In Proceedings of the Workshop on Dynamics, Optimization and Computation held in honor of the 60th birthday of Michael Dellnitz (pp. 31-65). Springer, Cham, 2020.
P. Gandhi, M. Golubitsky, C. Postlethwaite, I. Stewart and Y. Wang, Bifurcations on fully inhomogeneous networks, SIAM Journal on Applied Dynamical Systems, 19(1), 366-411 (46 pages), 2020.
M. Golubitsky and Y. Wang, Infinitesimal homeostasis in three-node input–output networks, Journal of Mathematical Biology, 1--23, 2020. Link

Sensitivity and uncertainty analysis using Latin hypercube sampling of parameter space and partial rank correlation coefficients for both proposed argasid tick models (Clifton et al., 2018)

Modeling the argasid tick life cycle and African Swine Fever (ASF) transmission

Unlike the well-studied hard-bodied (ixodid) ticks, soft-bodied (argasid) ticks exist in relative obscurity. The life cycle of ixodid ticks, the vectors for diseases like Rocky Mountain spotted fever and Lyme disease, have been characterized quantitatively, yet no mathematical model of any soft-bodied tick exists. This void is not trivial; argasid ticks such as Ornithodoros moubata are vectors of devastating human and animal diseases including African swine fever (ASF) in domesticated pigs and African relapsing fever in humans. Therefore, it is imperative to quantitatively understand the complex life cycle of this tick. We have proposed the first two mathematical models of the life cycle of O.~moubata to explore the dynamics and identify knowledge gaps of these poorly studied ticks. These models provide the basis for developing future models that include disease states to explore infection dynamics and possible management of ASF.

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