The phrase "a sequence of period" is not correct in English.
Did you mean "a sequence of periods"? You can use the corrected phrase when discussing a series of time intervals or events that occur in succession.
Example: "The project will be completed in a sequence of periods, each focusing on different phases of development."
Alternatives: "a series of periods" or "a succession of periods".
The PLL dynamics in the unstable region is found to have a sequence of period doubling bifurcation and chaos.
It is shown that with an increase in the amplitude of the forcing that quasiperiodic behaviour occurs, followed by a sequence of period doubling bifurcations leading to chaos.
Furthermore, the noise fluctuations of the system induce early transition to chaos for a system undergoing a sequence of period doubling bifurcations to chaos, and destabilize first the solution with "weaker protection" for a system having multiple stable steady state solutions.
The numerical simulation demonstrates that there exists a sequence of period-doubling bifurcation to chaos.
Moreover, it is found that the route to chaos is through a sequence of period-doubling bifurcations.
Two of the traveling waves lose their stability by Hopf bifurcation and have a sequence of period-doubling bifurcations leading to chaos.
The route to chaos in the first regime was attributed to a sequence of period-doubling bifurcations of the period-1 (synchronous) rotor response.
The period-3 orbit was also observed to undergo a sequence of period-doubling bifurcations resulting in chaotic vibrations of the rotor.
This method is illustrated here on a conservative, nonlinear Mathieu equation, for which a sequence of period-doubling bifurcations is followed, long enough to obtain accurate estimates of the two universal scaling constants α, β, as well as the universal rate δ, by which the bifurcation values of a parameter q = qk, k =1, 2, 3, …, tend to their limiting value, q∞ < ∞, as k increases.
Let (I_U) be an set of index entries over a sequence of periods of time (U).
We model the problem using a sequence of periods, each corresponding to a season.
