A three-dimensional angiogenesis model with time-delay

In this paper, we study the effect of time delays on dynamics angiogenesis tumor growth. The represent taken for mitosis. model is based reaction-diffusion equation described in form concentration nutrients $ \sigma and distribution internal pressure p caused by movement cells. vasculature supplies to tumor, so that \frac{\partial\sigma}{\partial {\bf{n}}}+\beta(\sigma-\bar{\sigma}) = 0 holds boundary, where a positive constant \beta rate nutrient supply \bar{\sigma} outside tumor. A parameter \mu expresses 'aggressiveness' It proved under non-radially symmetric perturbations, there exists \mu_{*}>0 such stationary solution linearly stable \mu<\mu_{*} $, unstable \mu>\mu_{*} $. Moreover, also found adding delay would lead large bigger proliferation intensity are, greater size.