1. Previous examination of the phase space of a mathematical model of a bursting molluscan neuron has demonstrated the existence of multiple stable oscillatory modes. The present study examined the extent to which multistability could be regulated by known modulatory agents, the consequences of that regulation on the response of the neuron to synaptic inputs, the effects of noise, and the potential of multistability to enrich the repertoire of neuromodulatory effects. 2. Coexisting stable attractors may appear when a change is made in a voltage-dependent conductance in a manner that simulates the application of a neuromodulator. A small transient perturbation can shift the model neuron between stable modes, greatly amplifying the original perturbation. Thus the model becomes more sensitive to conventional synaptic inputs. These mode shifts are robust in the presence of low-amplitude synaptic noise. 3. In response to random high-amplitude synaptic noise, a model neuron rendered multistable by a simulated application of a neuromodulator produces apparently random activity, whereas in response to the same synaptic noise, a monostable model neuron produces barely perturbed regular activity. Thus an increase in the number of attractors enhances sensitivity to both conventional synaptic inputs and noise. Conversely, a decrease is associated with a reduction in sensitivity. 4. The response of a neuron to a subsequent transient perturbation in the level of neuromodulator depends on the steady-state level of the neuromodulator. For example, if the steady-state level is associated with a multistable neuron, a mode shift produced by such a transient change in the level of neuromodulator (manifested in our model as a conductance change) can persist after the conductance is returned gradually to its original value. Thus multistable dynamic activity permits the effects of a neuromodulator to persist when the neuromodulator is no longer present. 5. The mechanism of mode shifting between coexisting stable oscillatory modes introduces a number of novel possibilities with potentially profound implications for information processing and storage in a single neuron.