Hybrid & impulsive systems
Stability, bifurcation, time delays, stochastic disturbances, and nonlinear dynamics.
Applied mathematics · Dynamical systems & control
Xinzhi Liu
Professor, Department of Applied Mathematics
University of Waterloo
Studying how complex systems evolve, interact, and can be controlled—from hybrid and impulsive systems to multi-agent networks and infectious disease models.
Xinzhi Liu · University of Waterloo
Research
Mathematics for connected, changing systems
My work develops theory and control methods for systems with switching, delays, impulses, and uncertainty, with applications across engineering and public health.
Multi-agent systems
Synchronization, consensus, formation control, and complex dynamical networks.
Control in practice
Vehicle platoons, infectious disease modeling, neural networks, and resilient control.
Scholarship
Publications & books
Browse the complete publication list, including journal articles, conference proceedings, monographs, edited volumes, and chapters.
Selected monographs
- Bifurcation Theory of Impulsive Dynamical SystemsWith Kevin Church · Springer, 2021
- Impulsive Systems on Hybrid Time DomainsWith Kexue Zhang · Springer, 2019
- Theory of Hybrid Systems: Deterministic and StochasticWith Mohamad Alwan · Springer, 2018
- Infectious Disease Modeling: A Hybrid System ApproachWith Peter Stechlinski · Springer, 2017
Research group
Students & collaborators
Mentoring graduate researchers and visiting scholars is a central part of my work.
Graduate students and visitorsProspective students
I welcome inquiries from prospective graduate students and visiting PhD students interested in dynamical systems, multi-agent control, complex networks, and epidemic modeling.
For application information and research areas, see the prospective student page.
Information for prospective studentsTeaching
Learning the language of dynamics
Courses in stability theory and applied mathematics connect rigorous analysis with the behavior of real systems.
Teaching pageAcademic background
Ph.D., University of Texas at Arlington. Professor in the Department of Applied Mathematics at the University of Waterloo since 1997.
Mini CVConnect
Let’s talk mathematics.
For research collaboration, graduate inquiries, and academic correspondence, please reach out by email.
Email Xinzhi LiuContact details
xzliu@uwaterloo.ca
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario, Canada N2L 3G1
Phone: +1 519 888 4567, ext. 36007