For standard definitions of attracting fixed point, saddle point, stable manifold, and related notions, see [8, 24].
Now, the trajectory leaves the branch of repelling periodic orbits for the branch of attracting fixed points.
As the parameter I increases further, the trajectory leaves the repelling branch sooner, eventually resulting in relaxation oscillations (Figure 1f), in which the trajectory spends O ( 1 ) time near both branches of attracting fixed points of the fast system.
The long-period bursting state in Figure 2c corresponds to a torus canard with head which spends long times near branches of both attracting and repelling periodic orbits of the fast system, but leaves the repelling branch for the branch of attracting fixed points of the fast system, corresponding to the onset of the inactive phase of the burst.
For example, it is possible to have a bursting orbit that follows the branch of attracting fixed points of the fast system down in u to the subcritical Hopf bifurcation and then spirals along the associated branch of repelling periodic orbits for some time.
When b 1 is sufficiently negative (i.e., sufficiently past the torus canard explosion), the trajectory does not follow the branch of repelling periodic orbits and instead transitions directly from the saddle-node of periodic orbits to the branch of attracting fixed points, resulting in a large amplitude sub-Hopf/fold cycle bursting orbit such as the one shown in Figure 4 at b 1 = − 0.162.
New points of view attract you, so you move toward them.
He pointed out that the benefit of attracting so many hits is that visitors are then able read other, more serious, items.
Our results suggest that uniformly attracting or repelling solutions are the true analogues of attracting or repelling fixed points of autonomous systems.
But pointing out that hypocrisy is Bruni's way of attracting money and attention to himself.
