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dc.contributor.authorYe, Mengbin
dc.contributor.authorLiu, J.
dc.contributor.authorAnderson, B.D.O.
dc.contributor.authorCao, M.
dc.identifier.citationYe, M. and Liu, J. and Anderson, B.D.O. and Cao, M. 2021. Applications of the Poincare-Hopf Theorem: Epidemic Models and Lotka-Volterra Systems. IEEE Transactions on Automatic Control.

This paper focuses on properties of equilibria and their associated regions of attraction for continuous-time nonlinear dynamical systems. The classical Poincar\'e--Hopf Theorem is used to derive a general result providing a sufficient condition for the system to have a unique equilibrium. The condition involves the Jacobian of the system at possible equilibria, and ensures the system is in fact locally exponentially stable. We apply this result to the susceptible-infected-susceptible (SIS) networked model, and a generalised Lotka--Volterra system. We use the result further to extend the SIS model via the introduction of decentralised feedback controllers, which significantly change the system dynamics, rendering existing Lyapunov-based approaches invalid. Using the Poincar\'e--Hopf approach, we identify a necessary and sufficient condition under which the controlled SIS system has a unique nonzero equilibrium (a diseased steady-state), and monotone systems theory is used to show this nonzero equilibrium is attractive for all nonzero initial conditions. A counterpart condition for the existence of a unique equilibrium for a nonlinear discrete-time dynamical system is also presented

dc.titleApplications of the Poincare-Hopf Theorem: Epidemic Models and Lotka-Volterra Systems
dc.typeJournal Article
dcterms.source.titleIEEE Transactions on Automatic Control

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curtin.departmentSchool of Electrical Engineering, Computing and Mathematical Sciences (EECMS)
curtin.accessStatusOpen access
curtin.facultyFaculty of Science and Engineering
curtin.contributor.orcidYe, Mengbin [0000-0003-1698-0173]
curtin.contributor.scopusauthoridYe, Mengbin [56203529600]

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