Codimension-two bifurcations analysis and tracking control on a discrete epidemic model

Na Yi, Qingling Zhang, Peng Liu, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)


In this paper, the dynamic behaviors of a discrete epidemic model with a nonlinear incidence rate obtained by Euler method are discussed, which can exhibit the periodic motions and chaotic behaviors under the suitable system parameter conditions. Codimension-two bifurcations of the discrete epidemic model, associated with 1:1 strong resonance, 1:2 strong resonance, 1:3 strong resonance and 1:4 strong resonance, are analyzed by using the bifurcation theorem and the normal form method of maps. Moreover, in order to eliminate the chaotic behavior of the discrete epidemic model, a tracking controller is designed such that the disease disappears gradually. Finally, numerical simulations are obtained by the phase portraits, the maximum Lyapunov exponents diagrams for two different varying parameters in 3-dimension space, the bifurcation diagrams, the computations of Lyapunov exponents and the dynamic response. They not only illustrate the validity of the proposed results, but also display the interesting and complex dynamical behaviors.
Original languageEnglish
Pages (from-to)1033-1056
Number of pages24
JournalJournal of Systems Science and Complexity
Issue number6
Publication statusPublished - 1 Dec 2011


  • Chaos
  • codimension-two bifurcations
  • discrete epidemic model
  • tracking control

ASJC Scopus subject areas

  • Information Systems
  • Computer Science (miscellaneous)


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