This paper is concerned with the mathematical modeling and analysis of
the multiplicity and autothermicity of steady states for a specific g
roup of chemically reacting systems. The group is exemplified by coupl
ed fluidized-bed reactors, where at least one is an exothermic reactor
. Three classes of such systems were analyzed, namely, reactor-heat-ex
changer, reactor cooperating with an autothermal heat exchanger and tw
o coupled fluidized-bed reactors. In the third case, an exothermic pro
cess is carried out in one reactor, but an endothermic process occurs
in the second one. In all three cases, solid particles of the catalyst
are assumed to circulate between the coupled reactors. A general meth
od of analysis of the multiplicity of steady states in such complex sy
stems will be presented. A large number of hysteresis loops of steady
states have been obtained. By the analysis of the position and shape o
f these, the influence of selected model parameters on the possibility
of the existence of a multiplicity of steady states has been determin
ed.