Abstract
In this paper, we consider a three-dimensional nonlinear delay differential system (tumor cells, cytotoxic-T lymphocytes, T-helper cells) with single interaction delay. We perform linear stability of the equilibria and the existence of Hopf bifurcation in which the discrete time delay is used as a bifurcation parameter. We estimate the length of delay to preserve the stability of period-1 limit cycle. We also investigate the direction, period, and the stability of bifurcated periodic solutions by applying normal form method and center manifold theory. We observe that the discrete time delay plays an important role in stability switching. Numerical simulations are presented to illustrate the rich dynamical behavior of the model with different values for the time delay τ including the existence of periodic oscillations, which demonstrate the phenomena of long-term tumor relapse.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
