## 3 Results
### Treadmill Gradient Effects on Local Dynamic Stability and Acceleration Magnitude  
The results indicate that the main effects of treadmill gradients on running stability, as assessed by the LyE of individual PMs (PPk_LyE), are predominantly observed in PM\({}_{3}\), corresponding to the mid-stance phase of the gait cycle (PP3_LyE: F(4,72) = 10.877, \(p<\) 0.001, \(\eta_{\text{p}}\)2 = 0.377, 1 - \(\beta\) = 1). Post hoc tests (Figure 2A) reveal that decline treadmill running results in higher instability compared to incline treadmill running. Specifically, running with a 6-degree decline exhibited a higher LyE value, indicating lower stability than running with both a 3-degree incline (\(p<\) 0.001, [PERSON]'s d = 1.162) and a 6-degree incline (\(p\) = 0.005, [PERSON]'s d = 1.176). Furthermore, running with a 3-degree decline also showed greater instability than running with a 3-degree incline (\(p\) = 0.003, [PERSON]'s d = 0.588). Post hoc tests revealed large effect sizes ([PERSON]'s d), indicating substantial differences in running stability (LyE) between conditions. Specifically, decline treadmill running, particularly at 6\({}^{\circ}\), exhibited large effect sizes when compared to the incline conditions, suggesting a marked decrease in stability during decline running.  
In terms of the acceleration magnitude of individual PMs (PAk_RMS), significant effects of treadmill gradients were noted in PM\({}_{2}\) (PA2_RMS: F(4,72) = 6.378, \(p<\) 0.001, \(\eta_{\text{p}}\)2 = 0.262, 1 - \(\beta\) = 0.986), PM\({}_{3}\) (PA3_RMS: F(4,72) = 31.170, \(p<\) 0.001, \(\eta_{\text{p}}\)2 = 0.634, 1 - \(\beta\) = 1), and PM\({}_{5}\) (PA5_RMS: F(4,72) = 2.933, \(p=\) 0.026, \(\eta_{\text{p}}\)2 = 0.140, 1 - \(\beta\) = 0.762). Post hoc analyses (Figure 2B) for PM\({}_{2}\) indicate that running on a flat treadmill (0 degrees) resulted in a greater RMS value compared to running with a 6-degree incline (\(p\) = 0.01, [PERSON]'s d = 0.754). For PM\({}_{3}\), running with a 6-degree incline exhibited a higher RMS value than running with a 3-degree incline (\(p<\) 0.001, [PERSON]'s d = 1.115), a 0-degree incline (\(p<\) 0.001, [PERSON]'s d = 1.630), a 3-degree decline (\(p<\) 0.001, [PERSON]'s d = 1.542). Additionally, running with a 3-degree decline showed a lower RMS value compared to running with a 3-degree incline (\(p\) = 0.003, [PERSON]'s d = 0.925), while running at 0 degrees had a lower RMS value than running with a 3-degree incline (\(p<\) 0.001, [PERSON]'s d = 0.945). Lastly, for PM\({}_{5}\), running with a 3-degree incline had a lower RMS value than running with a 6-degree incline (\(p\) = 0.006, [PERSON]'s d = 0.725). Post hoc tests revealed moderate to large effect sizes ([PERSON]'s d), indicating substantial differences in acceleration magnitude between conditions.  
Figure 2: Post hoc tests illustrating the effects of treadmill gradient on (**A**) running stability, measured by the largest Lyapunov exponent (LyE), and (**B**) acceleration magnitude, assessed by the root mean square (RMS), of the first five movement components (PM\({}_{1-5}\)) under incline, level, and decline conditions. Data are presented as mean \(\pm\) standard error, with significant differences marked at \(p\leq 0.01\). Treadmill gradients significantly affect running stability, with the mid-stance phase (PM\({}_{3}\)) showing the most impact. Decline running, particularly at 6\({}^{\circ}\), results in greater instability compared to incline running at 3\({}^{\circ}\) and 6\({}^{\circ}\). Treadmill gradients also significantly affect acceleration magnitude (RMS) in PM\({}_{2}\), PM\({}_{3}\), and PM\({}_{5}\). For PM\({}_{2}\), flat running showed higher RMS than running with a 6\({}^{\circ}\) incline. For PM\({}_{3}\), running with a 6\({}^{\circ}\) incline had the highest RMS, exceeding all other gradients, while a 3\({}^{\circ}\) decline and flat running had lower RMS values than running with a 3\({}^{\circ}\) incline. For PM\({}_{5}\), running with a 3\({}^{\circ}\) incline showed lower RMS than running with a 6\({}^{\circ}\) incline.