where V is the membrane potential, m, n, h are the gate variable, and [I.sub.ext] denotes an external forcing current, respectively.
At first, the autapse connection is switched off, the external forcing is imposed on neuron as [I.sub.ext] = 10.0 [micro]mol/L*[cm.sup.2] at t < 40 s, the calcium concentration of astrocyte and [IP.sub.3] is calculated at [mathematical expression not reproducible] = 0.2, and the results are plotted in Figure 1.
It is found that the membrane potential is decreased to quiescent state when the external forcing current is removed and the oscillating in [Ca.sup.2+] is also stabilized, the mechanism is that astrocyte and neuron are coupled with weak intensity, insufficient [IP.sub.3] is not effective to trigger continuous oscillation in calcium concentration, and the exchange of transmembrane current is suppressed.
When the external forcing current is removed, the concentration of [IP.sub.3] is decreased quickly because continuous release of neurotransmitter occurs in presence of external stimuli beyond threshold.
Furthermore, larger [mathematical expression not reproducible] (=0.8) is used to investigate the same problem by applying external forcing current [I.sub.e]xt = 10.0 [micro]mol/L*[cm.sup.2] with a transient period f = 40 s from beginning, and the results are plotted in Figure 6.
In case of large value setting for [mathematical expression not reproducible], [Ca.sup.2+] and [IP.sub.3] show slight oscillation in concentration when external forcing current is removed.
Mutual coupling between astrocyte and neuron driven by autapse can trigger complex stimuli for neuron, astrocyte by setting different external forcing currents, and time delay and feedback gain in autapse; as a result, the response of electrical activities becomes more complex.
In summary, autapse connection and driving, external forcing, and also the coupling between neuron and astrocyte all contribute the oscillating behavior for [Ca.sup.2+] by increasing the [IP.sub.3] concentration beyond the threshold to keep continuous oscillating in [Ca.sup.2+] concentration.
Based on our proposed new neuron model, it is found that autapse connection can also be helpful to change the oscillating behaviors for [Ca.sup.2+] and also the changes of [IP.sub.3]; as a result, electric response to external forcing and mode selection in neuron can be self-adaptive.
And the external forcing current regulates the neuron by [I.sub.ext] = 10.0 [micro]mol/L x [cm.sup.2] at t < 40 s.
And the external forcing current regulates the neuron by setting [I.sub.ext] = 10.0 [micro]mol/L*[cm.sup.2] at t < 40 s.