| Abstract: |
| Chemotaxis, the directed movement of cells or living organisms in response to the concentration gradient of chemical substances, plays a significant role in a large range of biological phenomena such as tumor growth, wound healing, and embryo development. One of the most important and interesting phenomena of chemotaxis is cellular aggregation, in which initially evenly distributed cells merge with each other and eventually aggregate into one or several groups. Mathematically, this phenomenon can be modeled by showing time-dependent solutions converge to bounded but spikey stationary solutions. In this talk, first, we will talk about the stability and instability of constant solution. Then, we will discuss the local bifurcation and stability of bifurcation solutions from the constant solution. Next, we will investigate global bifurcation and spiky bifurcation solutions. Finally, we will show some numerical simulations to visualize theoretical results and demonstrate some interesting cellular aggregation phenomena. |
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