Stability, bifurcation and spikes of stationary solutions in a chemotaxis system with singular sensitivity and logistic source (Q6610240)

In this paper, the authors investigated the stability, bifurcation and spikes of positive stationary solutions of a parabolic-elliptic chemotaxis system with singular sensitivity and logistic source. The stability conditions of the constant steady state, a local branch condition of nonconstant steady state near the constant steady state point were obtained. The spike solution was also yielded. Numerical simulations met their theoretical results well. The obtained results are quite wealthy and interested, one can figure out the complicated dynamics of the parabolic-elliptic chemotaxis systems to some extent based on these theoretical and numerical results.