Sentence examples for the period solution from inspiring English sources

Based on the research of the period solution in [36], we propose our optimal problem on the condition that (4.32) admits a periodic solution with period T. According to the theory in Section 2, we can rewrite system (4.32) on one period ((0,T)) as follows: left { textstylebegin{array}{l} left.

The stability of the period solutions is also examined in detail.

The residue harmonic balance method is used for generating the higher-order approximations to the angular frequency and the period solutions of above mentioned fractional oscillator.

In Equation 11, x 10 ′ ∗ x 0 is the change in the second period solution (without warning) with respect to x 0, and similarly x 11 ′ ∗ x 0 is the change in the second period solution (with a warning) with respect to x 0. Note that these first order conditions (Equations 8, 9, and 11) cannot be simultaneously satisfied.

In order to obtain a constant nanowire array growth rate, the solutions were refreshed during the reaction period (solution turnover time 2.5 h).

Afterwards, a stable periodic solution of period 2 appears, then the periodic solution of period 4 becomes unstable, and a periodic solution of period 8 appears and chaos happens.

Further, the complete expression of the period of the periodic solution is obtained.

As R 0 increases further, the periodic solution of period 4 becomes unstable, and a periodic solution of period 8 appears.

When R 0 passes through 226.8, the periodic solution of period 2 losses its stability, and a stable periodic solution of period four appears (see Figure 2(c)).

We can also find that the amplitude and period of the periodic solution will increase gradually as time delay increases.

The bifurcating periodic solutions are stable and the period of the periodic solutions increases.