Global Bifurcation And Stability Of Steady States For Stripe Formation In Bacterial Systems With Density-suppressed Motility

Stripe formation in bacterial systems described that Escherichia coli can excrete AHL in agar plates.But as the AHL concentration increases,the bacteria no longer diffuse,creating a stripe pattern.In this paper,we study partial differential equations describing this biological model.We first prove the existence of the local solution of the system of equations,and then use the abstract global bifurcation theorem to prove the existence of the local solution in the global.Then we study the stability of the bifurcation equilibrium,and give the necessary and sufficient condition of stability.Finally,we study the numerical simulation confirming the reliability of the necessary conditions.