Qualitative analysis on positive steady-state solutions for an autocatalysis model with high order

摘要: Abstract This paper is concerned with an autocatalysis model high order under Neumann boundary conditions. Firstly, the stability of equilibrium discussed and effect diffusion coefficients on Turing instability described. Next by maximum principle Poincare inequality, a priori estimates some characters positive steady-state solutions are given. Moreover, bifurcations at both simple double eigenvalues intensively investigated. Using bifurcation theory, we establish global structure from obtain conditions to determine direction. The techniques space decomposition implicit function theorem adopted deal case eigenvalues. Finally, numerical simulations shown supply supplement analytical results.