TABLE OF CONTENTS As basic unit to build up the CNN-based CPG a second-order CNN cell will be taken into consideration. This will be referred in the following as CNN neuron or CPG cell. More precisely, the following definition can be stated:
(The CNN cell-neuron.) The second-order CNN cell represented by the following equations:
| (2.5) |  |
where
| (2.6) |  |
with i=1, 2, , M, j=1, , N and k=1, 2 is the basic unit to build up the CNN-based CPG and is referred as the CNN neuron or the CPG cell.
The most important characteristics of Eq. (2.5) is that for a suitable choice of parameters it behaves as a nonlinear oscillator with slow-fast dynamics. In other words, Eq. (2.5) admits a stable limit cycle.
The CNN neuron of Eq. (2.5) with parameters as in Table 2.1 has a stable limit cycle with slow-fast dynamics.
|
| s | i 1 | i 2 |
|---|---|---|---|
| 0.5 | 1 | ?0.3 | 0.3 |
The behavior of the CNN neuron (2.5) can be accurately analyzed by considering the phase plane divided into nine different affine subspaces in which either all or some of the cell states are saturated or not, and examining the equilibria of these regions. The corresponding equilibria are indicated with subscripts relating to the partial saturated region (p) or saturated region (s) and superscripts relating to the value of the saturation...
