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For studying how dynamical responses to external stimuli depend on thesynaptic-coupling type, we consider two types of excitatory and inhibitorysynchronization (i.e., synchronization via synaptic excitation and inhibition)in complex small-world networks of excitatory regular spiking (RS) pyramidalneurons and inhibitory fast spiking (FS) interneurons. For both cases ofexcitatory and inhibitory synchronization, effects of synaptic couplings ondynamical responses to external time-periodic stimuli $S(t)$ (applied to afraction of neurons) are investigated by varying the driving amplitude $A$ of$S(t)$. Stimulated neurons are phase-locked to external stimuli for both casesof excitatory and inhibitory couplings. On the other hand, the stimulationeffect on non-stimulated neurons depends on the type of synaptic coupling. Theexternal stimulus $S(t)$ makes a constructive effect on excitatorynon-stimulated RS neurons (i.e., it causes external phase lockings in thenon-stimulated sub-population), while $S(t)$ makes a destructive effect oninhibitory non-stimulated FS interneurons (i.e., it breaks up originalinhibitory synchronization in the non-stimulated sub-population). As results ofthese different effects of $S(t)$, the type and degree of dynamical response(e.g., synchronization enhancement or suppression), characterized by thedynamical response factor $D_f$ (given by the ratio of synchronization degreein the presence and absence of stimulus), are found to vary in a distinctlydifferent way, depending on the synaptic-coupling type. Furthermore, we alsomeasure the matching degree between the dynamics of the two sub-populations ofstimulated and non-stimulated neurons in terms of a "cross-correlation" measure$M_c$. With increasing $A$, based on $M_c$, we discuss the cross-correlationsbetween the two sub-populations, affecting the dynamical responses to $S(t)$.

Dynamical Responses to External Stimuli for Both Cases of Excitatory and Inhibitory Synchronization in A Complex Neuronal Network