Nonlinear Dynamics

, Volume 67, Issue 1, pp 629–640 | Cite as

Hopf bifurcation analysis in a delayed oncolytic virus dynamics with continuous control

  • Shaoli Wang
  • Shuli Wang
  • Xinyu SongEmail author
Original Paper


A delayed oncolytic virus dynamics with continuous control is investigated. The local stability of the infected equilibrium is discussed by analyzing the associated characteristic transcendental equation. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. Using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. Numerical simulations are carried out to support the theoretical results.


Oncolytic virus dynamics Time delay Hopf bifurcation Periodic solution 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.College of ScienceXi’an Jiaotong UniversityXi’anChina
  2. 2.School of Computer and Information TechnologyXinyang Normal UniversityXinyangChina
  3. 3.College of Mathematics and Information ScienceXinyang Normal UniversityXinyangChina

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