Multistability of a Two-Dimensional Map Arising in an Influenza Model

Yu Jhe Huang, Hsuan Te Huang, Jonq Juang*, Cheng Han Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper, we propose and analyze a nonsmoothly two-dimensional map arising in a seasonal influenza model. Such map consists of both linear and nonlinear dynamics depending on where the map acts on its domain. The map exhibits a complicated and unpredictable dynamics such as fixed points, period points, chaotic attractors, or multistability depending on the ranges of a certain parameters. Surprisingly, bistable states include not only the coexistence of a stable fixed point and stable period three points but also that of stable period three points and a chaotic attractor. Among other things, we are able to prove rigorously the coexistence of the stable equilibrium and stable period three points for a certain range of the parameters. Our results also indicate that heterogeneity of the population drives the complication and unpredictability of the dynamics. Specifically, the most complex dynamics occur when the underlying basic reproduction number with respect to our model is an intermediate value and the large portion of the population in the same compartment changes in states the following season.

Original languageEnglish
Article number15
JournalJournal of Nonlinear Science
Issue number1
StatePublished - Feb 2022


  • Chaotic attractors
  • Multistability
  • Nonsmoothly two-dimensional map
  • Periodic points
  • Seasonal influenza model


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