Abstract: The mechanism of bifurcations for the thermal convection flow of porousmedia is studied by analytical method.It is pointed out that the Rayleigh number Ra in thenonlinear flow equations is an important parameter to determine the fiow characteristics。If Ra is less than the critical Rayleigh number Ra_c,the fluid in the porous medium is instatic state,which is stable.If Ra>Ra_c,the solution of the flow equations in the porousmedia will bifurcate.There are a lot of criticaI Rayleigh numbers,and we can write th...