2,312 publications from this institution
To find the exact explicit solution of the concatenation model, the corresponding differential system of the amplitude component is used, which is a planar dynamical system with a singular straight line. In this paper, by using the techniques from dynamical systems and singular traveling wave theory developed by Li and Chen [2007], its corresponding traveling wave system is solved and analyzed, obtaining the corresponding phase portraits and showing the dynamical behavior of the amplitude component. Under different parameter conditions, exact explicit solitary wave solutions, periodic wave solutions, kink and anti-kink wave solutions, compacton solutions, as well as peakons and periodic peakons, are found explicitly.
The loss of complexity in ageing hypothesis (LOCH) has found support from EEG studies, most of which adopted signal-domain complexity measures. The present study adopted the largest Lyapunov exponent (LLE) to measure complexity from a nonlinear dynamical systems perspective. A total of 144 participants were included and divided into young, young-old and old-old groups. Both sensor-space and source-space results showed significantly lower LLE for older than younger adults. The age-related differences were region-dependent, being most prominent in the frontal region, followed by bilateral temporal regions. The occipital region showed non-significant differences. Significant reduction of LLE in the posterior cingulate was also observed by virtue of the source-space analysis. We also evaluated the relationships between LLE and other complexity measures. The most intriguing result was the negative correlation between LLE and Lempel-Ziv complexity (LZC). The age-related decrease in LLE indicated a higher regularity in dynamics, while the higher LZC indicated a higher randomness in the signal domain. The new findings support the LOCH by demonstrating the simultaneous increase in regularity and randomness.
