Table 2.
Achievable output differences for different input profiles.
| ||u||2 = 1 | (A, I, R*) | I | R* |
|---|---|---|---|
| Sine | 0.472 | 0.472 | 0.0195 |
| Sine w. exp. mult. | 0.475 | 0.474 | 0.0209 |
| Cosine or (10) | 0.473 | 0.472 | 0.0200 |
| Square wave | 0.451 | 0.450 | 0.0182 |
| Sinc | 0.412 | 0.412 | 0.0153 |
| Constant | 0.198 | 0.197 | 0.0070 |
| ||u||2 = 0.01 | (A, I, R*) | I | R* |
| Sine | 0.476 | 0.481 | 0.0203 |
| Sine w. exp. mult. | 0.467 | 0.467 | 0.0195 |
| Cosine or (10) | 0.457 | 0.456 | 0.0191 |
| Square wave | 0.441 | 0.441 | 0.0184 |
| Sinc | 0.396 | 0.396 | 0.0173 |
| Constant | 0.198 | 0.198 | 0.0085 |
Numerical estimates of maxu ||y1 - y2||2/||u||2 with different inputs for the Dictyostelium models by simulating the nonlinear system. Here maximization is over different frequencies for inputs where frequency makes sense. Output is either all states or I or R*.