The phrase "arbitrary period" is correct and usable in written English.
It can be used to refer to a time frame that is chosen without any specific reason or criteria, often in discussions about time management or scheduling.
Example: "The project deadline was set for an arbitrary period, leading to confusion among team members about the timeline."
Alternatives: "random timeframe" or "unspecified duration".
Since the equilibrium could be viewed as the periodic solution of arbitrary period, as a consequence of Theorems 3.1, 4.1 and 4.2, we obtain the following corollary.
It is shown that the proposed controller can achieve stability for an arbitrary unstable fixed point (UPF) or unstable periodic orbit (UPO) with arbitrary period.
i) Arbitrarily small difference of initial conditions may cause a large deviation of long-term iterations; ii) There may be many periodic points with almost arbitrary period.
For example: i) Arbitrarily small difference of initial conditions may cause a large deviation of long-term iterations; ii) There may be many periodic points with almost arbitrary period.
An equilibrium point can be looked as a special periodic solution of neural networks with arbitrary period.
For example, in [2] Sun et al. investigate the emergence of quasi-periodic and mode-locked states of an arbitrary period in pairs of coupled maps of a discrete system.
To limit the length of the canonical schedules and predict their task execution, tasks with arbitrary periods are first transformed into harmonic periods and their key features are profiled.
Additionally, they allow us to implement FBMC transmitters for any configuration of signal parameters (i.e., for arbitrary subcarrier period P, symbol period Nss, pulse shape length L g, and normalized subcarrier spacing Q) just by using simple digital signal processing blocks such as up/down-sampling converters, filters, and sample delays.
At a cell in which n earthquakes have occurred in the arbitrary determined period, i.e., a reference period Tr, assume λ n to be the expected number of earthquakes that will occur in the forecast period T. The value of λ n may be considered to be the product of an average activity per unit time (n/Tr) and the duration of the forecast period (T).
If you just measure performance over an arbitrary time period of, say, five years, you don't capture this point.
