test case $i$ | $1$ | $2$ | $3$ | $4$ | $5$ |
factor $\kappa_i$ | $1-10^{-16}$ | $1-10^{-8}$ | $1-10^{-4}$ | $1-10^{-2}$ | $1-10^{-1}$ |
In previous work [
Citation: |
Figure 2. Canard cycles with two breaking parameters, at level $\epsilon = 0$. (a) One jump breaking mechanism, with two jump points $\mathcal{C}_1^1$ and $\mathcal{C}_1^2$, and one Hopf breaking mechanism with a turning point $\mathcal{C}_2$. (b) Two Hopf mechanisms with turning points $\mathcal{C}_1$ and $\mathcal{C}_2$
Table 1.
Factors
test case $i$ | $1$ | $2$ | $3$ | $4$ | $5$ |
factor $\kappa_i$ | $1-10^{-16}$ | $1-10^{-8}$ | $1-10^{-4}$ | $1-10^{-2}$ | $1-10^{-1}$ |
Table 2. Numerically computed box dimensions
example system | (11) | (12) | (13) |
theoretical box dim. | $0$ | $1/2$ | 0 |
num. of digits of prec. | 170 | 60 | 150 |
computed orbit size $M$ | 500 | 10000 | 2000 |
test case $1$ box dim. | $0.019946$ | $0.499413$ | $0.031357$ |
test case $2$ box dim. | $0.021066$ | $0.498836$ | $0.033703$ |
test case $3$ box dim. | $0.021675$ | $0.521252$ | $0.035013$ |
test case $4$ box dim. | $0.021993$ | $0.532500$ | $0.035706$ |
test case $5$ box dim. | $0.022166$ | $0.532658$ | $0.036062$ |
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The fast subsystem
Canard cycles with two breaking parameters, at level
The numerical estimate of the box dimension depending on the number of calculated orbit values
The numerical estimate of the box dimension depending on the number of calculated orbit values
The numerical estimate of the box dimension depending on the number of calculated orbit values