  In this paper, we are concerned with the stability of heteroclinic cycles of
the symmetric May-Leonard competition model with seasonal succession.
Sufficient conditions for stability of heteroclinic cycles are obtained.
Meanwhile, we present the explicit expression of the carrying simplex in a
special case. By taking \phi as the switching strategy parameter for a given
example, the bifurcation of stability of the heteroclinic cycle is
investigated. We also find that there are rich dynamics (including nontrivial
periodic solutions, invariant closed curves and heteroclinic cycles) for such a
new system via numerical simulation. Biologically, the result is interesting as
a caricature of the complexities that seasonal succession can introduce into
the classical May-Leonard competitive model.
