Sentence examples for attracting cycle from inspiring English sources

While a proceeds to the outside of an (O varepsilon ))-neighbourhood of 0, it encounters the relaxation-like attracting cycle that surrounded all repelling cycles.

The attracting cycle is ({-1,0}) and Δ is a union of two small disks centered around the points of this cycle.

For each attracting cycle, we consider the union (V_{i}) of sufficiently small disks centered around the points of the cycle, such that (V_{i}) is contained in the immediate basin of attraction and (p(V_{i})) is relatively compact in (V_{i}).

Maistrenko, Y. Maistrenko, V.L., Vikul, S.I., Chua, L.O. "Bifurcations of attracting cycles from time-delayed Chua's circuit," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.5, no.3, pp.653-671.

Moreover, all critical points of p are attracted to attracting cycles, and the number of attracting cycles is bounded above by (d-1), by the Fatou-Shishikura inequality.

Set (Delta= bigcup_{i=1}^{k} V_{i}), where k is the number of attracting cycles.

In other words, the system has only one stable state, and no attracting cycles.

An alternative (non isochronal) framework for studying oscillators with an attracting limit cycle is to make a transformation to a moving orthonormal coordinate system around the limit cycle where one coordinate gives the phase on the limit cycle while the other coordinates give a notion of distance from the limit cycle.

Sufficient conditions of global attracting limit cycle existence for Lurie system with sign nonlinearity are presented.

A typical timeseries showing an attracting heteroclinic cycle for this system is shown in Figure 1.

Moreover, the numerical results showed the appearance of an attracting limit cycle of model (3).