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dc.contributor.authorYe, Mengbin
dc.contributor.authorLiu, J.
dc.contributor.authorAnderson, B.D.O.
dc.contributor.authorCao, M.
dc.date.accessioned2021-04-16T01:14:55Z
dc.date.available2021-04-16T01:14:55Z
dc.date.issued2021
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.
dc.identifier.urihttp://hdl.handle.net/20.500.11937/83245
dc.identifier.doi10.1109/TAC.2021.3064519
dc.description.abstract

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.relation.sponsoredbyhttp://purl.org/au-research/grants/arc/DP160104500
dc.relation.sponsoredbyhttp://purl.org/au-research/grants/arc/DP190100887
dc.titleApplications of the Poincare-Hopf Theorem: Epidemic Models and Lotka-Volterra Systems
dc.typeJournal Article
dcterms.source.issn0018-9286
dcterms.source.titleIEEE Transactions on Automatic Control
dc.date.updated2021-04-16T01:14:54Z
curtin.note

Copyright © 2021 IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.

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]
dcterms.source.eissn1558-2523
curtin.contributor.scopusauthoridYe, Mengbin [56203529600]


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