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When the problem has many solutions, it is guaranteed that, for any initial point, the trajectory of the network does converge to an exact solution of the problem.
The road might be long, and it will certainly be difficult, but only two things are certain at this point: the trajectory toward a one-state outcome becomes clearer by the minute and the use of force will not help Israelis get there safely.
At the torus bifurcation point, the trajectory resembles the periodic orbit at the saddle-node of periodic orbits (SNp) of the fast system.
The trajectory falls to the lower branch of the shifted manifold, slowly approaching eq ¯ 3. Once the inhibitory current is removed, the critical manifold shifts back to its original position, at which point the trajectory rapidly shoots in the direction of positive v.
At that point, the trajectory becomes periodic because the simulation is deterministic on a finite state space.
When the future direction changes from the expectation at the decision point, the trajectory shifts to the corresponding one (red dashed lines, VD2, VD4).
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Then given a time window that consists of time points, the trajectory of node of is denoted as.
When it falls inward toward the branch of fixed points, the trajectory resembles the bursting and torus canard with head trajectories seen at slightly larger k values.
Therefore, in this algorithm, the number of candidate points that the trajectory point has at most is determined as 5 by combining the running time and the matching precision. .
As stated before, the cross point would correspond to the vanishing point of the trajectory.
For convenience, we define the end-point mapping to describe the final point of the trajectory solution of the control system (1).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com