We study minimal multistable systems of coupled model neurons with
combined excitatory and inhibitory connections. With slow potassium
currents, multistability of several firing regimes with
distinctively different firing rates is observed. In the presence of
noise, there is noise-driven switching between these states of which
transient dynamics have 1/f-type power spectra. The selection between higher- and lower-frequency oscillations depends on external inputs, which results in coherence between the periodic input and the system's firing rate. Without slow potassium currents, there are multistable solutions in which two inhibitory neurons fire
synchronously or anti-synchronously. Addition of a small amount of
noise results in increased synchronizability of the two neurons
depending on the level of external inputs. These results suggest
adaptable dynamics of multistable neural attractors to external
inputs enhanced by additional noise.
We study a system of globally coupled FitzHugh-Nagumo equations as a stochastic resonator. Each unit is either excitatory or inhibitory. If the numbers of units of both types are nearly equal (balanced coupling), we observe the presence of multistable oscillatory states with different excitation or firing rates. In the presence of noise, random transitions between high- and low-frequency oscillatory states are observed and the resultant firing pattern is long-range correlated. Compared to other coupling types, the system demonstrates considerably improved rate-coding ability for both subthreshold and suprathreshold signals, even with a tiny level of noise.
Human cardiovascular and/or cardio-respiratory systems are shown
to exhibit both multifractal and synchronous dynamics, and we
recently developed a nonlinear, physiologically plausible model
for the synchronization between heartbeat and respiration
(Kotani, et al. Phys. Rev. E 65: 051923, 2002). By using the same model, we now show the multifractality in the heart rate dynamics. We find that beat-to-beat monofractal noise (fractional Brownian motion) added to the brain stem cardiovascular areas results in significantly broader singularity spectra for heart rate
through interactions between sympathetic and parasympathetic
nervous systems. We conclude that the model proposed here would
be useful in studying the complex cardiovascular and/or cardio-
respiratory dynamics in humans.