Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter.

The inherent non-smoothness of the vibroimpact system leads to complex behaviors and a strong sensitivity to parameter changes. Unfortunately, uncertainties and errors in system parameters are inevitable in mechanical engineering. Therefore, investigations of dynamical behaviors for vibroimpact systems with stochastic parameters are highly essential. The present study aims to analyze the dynamical characteristics of the three-degree-of-freedom vibroimpact system with an uncertain parameter by means of the Chebyshev polynomial approximation method. Specifically, the vibroimpact system model considered is one with unilateral constraint. Firstly, the three-degree-of-freedom vibroimpact system with an uncertain parameter is transformed into an equivalent deterministic form using the Chebyshev orthogonal approximation. Then, the ensemble means responses of the stochastic vibroimpact system are derived. Numerical simulations are performed to verify the effectiveness of the approximation method. Furthermore, the periodic and chaos motions under different system parameters are investigated, and the bifurcations of the vibroimpact system are analyzed with the Poincaré map. The results demonstrate that both the restitution coefficient and the random factor can induce the appearance of the periodic bifurcation. It is worth noting that the bifurcations fundamentally differ between the stochastic and deterministic systems. The former has a bifurcation interval, while the latter occurs at a critical point.

Disrupted topological organization of the motor execution network in Wilson's disease.

Objective: There are a number of symptoms associated with Wilson's disease (WD), including motor function damage. The neuropathological mechanisms underlying motor impairments in WD are, however, little understood. In this study, we explored changes in the motor execution network topology in WD. Methods: We conducted resting-state functional magnetic resonance imaging (fMRI) on 38 right-handed individuals, including 23 WD patients and 15 healthy controls of the same age. Based on graph theory, a motor execution network was constructed and analyzed. In this study, global, nodal, and edge topological properties of motor execution networks were compared. Results: The global topological organization of the motor execution network in the two groups did not differ significantly across groups. In the cerebellum, WD patients had a higher nodal degree. At the edge level, a cerebello-thalamo-striato-cortical circuit with altered functional connectivity strength in WD patients was observed. Specifically, the strength of the functional connections between the cerebellum and thalamus increased, whereas the cortical-thalamic, cortical-striatum and cortical-cerebellar connections exhibited a decrease in the strength of the functional connection. Conclusion: There is a disruption of the topology of the motor execution network in WD patients, which may be the potential basis for WD motor dysfunction and may provide important insights into neurobiological research related to WD motor dysfunction.