Bifurcation and pattern formation of a tumor–immune model with time-delay and diffusion

Yunfeng Jia

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 178, issue C, 92-108

Abstract: A tumor–immune model with time-delay and diffusion is considered. Firstly, the local stability of equilibria and the existence of Hopf bifurcation are studied. Secondly, the direction and stability of Hopf bifurcation are discussed. Finally, the numerical simulations are used to verify the effectiveness of the theoretical results. It is found that the time-delay can destroy the stability of positive equilibrium and then affect the occurrence of Hopf branch. Specifically, the equilibrium is stable if the model is without delay or with small delay, and so there is no bifurcation; Conversely, when the delay is large, it induces the instability of equilibrium and the Hopf bifurcation occurs, the model then exhibits rich spatiotemporal dynamics.

Keywords: Tumor–immune model; Time-delay; Stability; Hopf bifurcation; Pattern formation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:178:y:2020:i:c:p:92-108

DOI: 10.1016/j.matcom.2020.06.011

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