  Nonlinear dynamical systems possessing reflection symmetry have an invariant
subspace in the phase space. The dynamics within the invariant subspace can be
random or chaotic. As a system parameter changes, the motion transverse to the
invariant subspace can lose stability, leading to on-off intermittency. Under
certain conditions, the bursting behavior is symmetry-breaking. We demonstrate
the possibility of observing multiplicative noise(chaos)-induced amplification
of weak signal and stochastic resonance via on-off intermittency with symmetry
breaking in a general class of symmetrical systems. Differences of this
mechanism of stochastic resonance to that in noisy bistable or threshold
systems are discussed
