ABSTRACT
In this paper, we investigate the mathematical models of discrete memristors based on Caputo fractional difference and G-L fractional difference. Specifically, the integer-order discrete memristor is a special model of those two cases. The "∞"-type hysteresis loop curves are observed when input is the bipolar periodic signal. Meanwhile, numerical analysis results show that the area of hysteresis decreases with the increase of frequency of input signal and the decrease of derivative order. Moreover, the memory effect, characteristics and physical realization of the discrete memristors are discussed, and a discrete memristor with short memory effects is designed. Furthermore, discrete memristive systems are designed by introducing the fractional-order discrete memristor and integer-order discrete memristor to the Sine map. Chaos is found in the systems, and complexity of the systems is controlled by the parameter of the memristor. Finally, FPGA digital circuit implementation is carried out for the integer-order and fractional-order discrete memristor and discrete memristive systems, which shows the potential application value of the discrete memristor in the engineering application field.
ABSTRACT
Background: There are limited sensitive evaluation methods to distinguish people's symptoms of peripheral fatigue and central fatigue simultaneously. The purpose of this study is to identify and evaluate them after acute exercise with a simple and practical scale. Methods: The initial scale was built through a literature review, experts and athlete population survey, and a small sample pre-survey. Randomly selected 1,506 students were evaluated with the initial scale after exercise. Subjective fatigue self-assessments (SFSA) were completed at the same time. Results: The Acute Exercise-Induced Fatigue Scale (AEIFS) was determined after performing a factor analysis. In the exploratory factor analysis, the cumulative variance contribution rate was 65.464%. The factor loadings of the total 8 questions were 0.661-0.816. In the confirmatory factor analysis, χ2/df = 2.529, GFI = 0.985, AGFI = 0.967, NFI = 0.982, IFI = 0.989, CFI = 0.989, and RMSEA = 0.048. The Cronbach's alpha coefficient for the scale was 0.872, and it was 0.833 for peripheral fatigue and 0.818 for central fatigue. The intra-class correlation coefficient for the scale was 0.536, and the intra-class correlation coefficients for peripheral fatigue and central fatigue were 0.421 and 0.548, respectively. The correlation coefficient between the total score of the AEIFS and the SFSA score was 0.592 (p < 0.01). Conclusion: Our results demonstrate that the AEIFS can distinguish peripheral fatigue and central fatigue and can also reflect their correlation. This scale can be a useful evaluation tool not only for measuring fatigue after acute exercise but also for guiding reasonable exercise, choosing objective testing indicators, and preventing sports injuries resulting from acute exercise-induced fatigue.
