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Quasiperiodic signal is ubiquitous and entrenched in neuronal networks, and thus taking it into consideration is necessary. The Wiener process with the intensity of σ is used here to model randomly fluctuated phase in external weak quasiperiodic signal. The departure from the normal periodicity can be governed by the parameter σ. Then, the effects of randomly fluctuated phase of signal and time-periodic coupling intensity of synaptic junctions between neurons on propagation of weak quasiperiodic signal through feed-forward Hodgkin–Huxley network are explored in detail. Increasing σ makes more neurons fire simultaneously, and better synchronous state is observed. Consequently, the external weak quasiperiodic signal introduced into all neurons in the first layer can be effectively transmitted through the whole feed-forward network via synchronization mechanism. In the case of time-periodic synaptic coupling intensity, when oscillatory frequency of synaptic coupling intensity is equal precisely to average frequency of external quasiperiodic signal, the propagation of weak quasiperiodic signal is optimal. Additionally, rapid oscillation of synaptic coupling intensity hinders or even kills the propagation of quasiperiodic signal to great depths of neuronal network, provided σ is not large enough.

Weak Quasiperiodic Signal Propagation through Multilayer Feed-Forward Hodgkin–Huxley Neuronal Network