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

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Abstract

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.

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Authors and Affiliations

  1. College of Science, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Shaoli Wang

  2. School of Computer and Information Technology, Xinyang Normal University, Xinyang, 464000, Henan, China

    Shuli Wang

  3. College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000, Henan, China

    Xinyu Song

Authors
  1. Shaoli Wang
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  2. Shuli Wang
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  3. Xinyu Song
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Corresponding author

Correspondence to Xinyu Song.

Additional information

Supported by the National Natural Science Foundation of China (Nos. 10971166, 10771179), the Innovation Scientists and Technicians Troop Construction Projects of Henan Province (104200510011) and program for Innovative Research Team (in Science and Technology) in University of Henan Province (2010IRTSTHN006).

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Wang, S., Wang, S. & Song, X. Hopf bifurcation analysis in a delayed oncolytic virus dynamics with continuous control. Nonlinear Dyn 67, 629–640 (2012). https://doi.org/10.1007/s11071-011-0015-5

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  • DOI: https://doi.org/10.1007/s11071-011-0015-5

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