FIGURE 4.5-7 "Burst-sharpening" behavior of the Szentagothai system. Traces: 1, Na (input); 2, Nb (input); 3, N1 (output); 4, N2 (output); 5, N3 (interneuron): 6, N4 (interneuron). The instantaneous frequency of the inputs is sinusoidally modulated 180° out of phase. The system generates short, six-pulse output bursts, 180° out of phase. It behaves as an input burst sharpener, rather than a true pattern generator.

and Eb = B * [1 - cos(rao t)] to FM spike trains. The Simnon program, SZGRIsys.t, to simulate the Szentagothai RI circuit is listed in Appendix 2. Figure 4.5-7 shows the spikes elicited from the four model neurons, and the input spike trains. Curiously, this RI system makes the bursts from N1 and N2 (traces 3 and 4) shorter and more regular, and it preserves the 180° phase shift in the FM inputs.

4.5.3 A simple Burst Generator

It is possible to use the recurrent feedback concept to generate alternate output spike bursts from a constant activation input spike train. However, symmetrical positive feedback RI, as described above is not used. Figure 4.5-8 illustrates such a system, proposed by the author. This system works because the output of neuron N1 is chopped by the delayed, local, high-gain, negative feedback from inhibitory inter-neuron, N2. Inhibitory interneuron N4, driven from the N1 output, keeps N2 from firing, thus producing alternate bursts of spikes from N1 and N2. (In linear control theory, a delay in a high-gain, negative feedback loop can destabilize the system, causing limit cycle oscillations, Ogata, 1990.) The Simnon program, BURSTNM1.t, for this bursting system is listed in Appendix 3.

Figure 4.5-9 illustrates the ability of this neural model to generate a two-phase, patterned output from N1 and N2, given a common, constant frequency source of spike excitation to N1 and N2. This architecture is a candidate for a central pattern generator (CPG) (Kleinfeld and Sompolinsky, 1989).

FIGURE 4.5-8 Model of the author's CPG system. Again, two output neurons and two interneurons are used. However, this system uses a single, delayed, negative feedback loop to obtain a 180° bursting output. The Simnon program, BURSTNM1.T , that simulates this system is given in Appendix 3.

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