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We apply the refined composite multiscale entropy (MSE) method to a one-dimensional directed small-world network composed of nodes whose states are binary and whose dynamics obey the majority rule. We find that the resulting fluctuating signal becomes dynamically complex. This dynamical complexity is caused (i) by the presence of both short-range connections and long-range shortcuts and (ii) by how well the system can adapt to the noisy environment. By tuning the adaptability of the environment and the long-range shortcuts we can increase or decrease the dynamical complexity, thereby modeling trends found in the MSE of a healthy human heart rate in different physiological states. When the shortcut and adaptability values increase, the complexity in the system dynamics becomes uncorrelated.

Intermittent dust acoustic wave turbulence self-excited by downward ion flow in dissipative dusty plasma is experimentally observed and investigated. The power spectra of the temporal dust density fluctuation show distinct bumps in the low-frequency regime and power-law scaling in the high-frequency regime. The structure-function analysis demonstrates the multifractal dynamics of the wave turbulence. Decreasing dissipation by decreasing neutral pressure leads to a more turbulent state with a less distinct low-frequency bump in the power spectrum, more stretched non-Gaussian tails in the histogram of the wave-height increment at a small time interval $\ensuremath{\tau}$, and a higher degree of multifractality. The loss of long time memory with increasing $\ensuremath{\tau}$ for a more turbulent state causes a change from the distribution with stretched non-Gaussian tails to Gaussian with increasing $\ensuremath{\tau}$.

We experimentally investigate the micro-origin of the absence of trough trapping in nonlinear traveling dust acoustic waves self-excited by the downward ion flow in the dissipative dusty plasma. The wave forms of dust density, the drag force from the background neutrals, ions, and dusts, and the effective potential energy for dusts are constructed by tracking dust motion and measuring the velocity and the position-dependent forces. The tilted washboard type potential wave form with a slight phase lead to the dust density wave form is obtained. It provides sufficient kinetic energy to compensate drag dissipation and move dusts from the dust density trough to the crest front. The dusts with sufficient energy overcome the downward pushing by the crest front, climb over the crest, and sustain the oscillatory motion with upward drift. Those dusts with insufficient energy to climb over the potential barrier of the crest are trapped in and move downward with the crest front, until kicked upward by fluctuation. The upward neutral dominated drag force prevents them from sliding down the potential energy hill at the crest front and further oscillating in the trough. It leads to the absence of trough trapping.