In this paper, the phase-portraits of plane homogeneous polynomial vector fields are studied and some formulae for the calculation of the number of different global phase-portraits of plane homogeneous polynomial vect...In this paper, the phase-portraits of plane homogeneous polynomial vector fields are studied and some formulae for the calculation of the number of different global phase-portraits of plane homogeneous polynomial vector fields are given. Some necessary and sufficient conditions for the global stability of these vector fields are derived.展开更多
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ...For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.展开更多
Individuals with NGLY1 Deficiency, an inherited autosomal recessive disorder, exhibit hyperkinetic movements including athetoid, myoclonic, dysmetric, and dystonic movements impacting both upper and lower limb motion....Individuals with NGLY1 Deficiency, an inherited autosomal recessive disorder, exhibit hyperkinetic movements including athetoid, myoclonic, dysmetric, and dystonic movements impacting both upper and lower limb motion. This report provides the first set of laboratory-based measures characterizing the gait patterns of two individuals with NGLY1 Deficiency, using both linear and non-linear measures, during treadmill walking, and compares them to neurotypical controls. Lower limb kinematics were obtained with a camera-based motion analysis system and bilateral time normalized lower limb joint time series waveforms were developed. Linear measures of joint range of motion, stride times and peak angular velocity were obtained, and confidence intervals were used to determine if there were differences between the patients and control. Correlations between participant and control mean joint waveforms were calculated and used to evaluate the similarities between patients and controls. Non-linear measures included: joint angle-angle diagrams, phase-portrait areas, and continuous relative phase (CRP) measures. These measures were used to assess joint coordination and control features of the lower limb motion. Participants displayed high correlations with their control counterparts for the hip and knee joint waveforms, but joint motion was restricted. Peak angular velocities were also significantly less than those of the controls. Both angle-angle and phase-portrait areas were less than the controls although the general shapes of those diagrams were similar to those of the controls. The NGLY1 Deficient participants’ CRP measures displayed disrupted coordination patterns with the knee-ankle patterns displaying more disruption than the hip-knee measures. Overall, the participants displayed a functional walking pattern that differed in many quantitative ways from those of the neurotypical controls. Using both linear and non-linear measures to characterize gait provides a more comprehensive and nuanced characterization of NGLY1 gait and can be used to develop interventions targeted toward specific aspects of disordered gait.展开更多
文摘In this paper, the phase-portraits of plane homogeneous polynomial vector fields are studied and some formulae for the calculation of the number of different global phase-portraits of plane homogeneous polynomial vector fields are given. Some necessary and sufficient conditions for the global stability of these vector fields are derived.
文摘For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.
文摘Individuals with NGLY1 Deficiency, an inherited autosomal recessive disorder, exhibit hyperkinetic movements including athetoid, myoclonic, dysmetric, and dystonic movements impacting both upper and lower limb motion. This report provides the first set of laboratory-based measures characterizing the gait patterns of two individuals with NGLY1 Deficiency, using both linear and non-linear measures, during treadmill walking, and compares them to neurotypical controls. Lower limb kinematics were obtained with a camera-based motion analysis system and bilateral time normalized lower limb joint time series waveforms were developed. Linear measures of joint range of motion, stride times and peak angular velocity were obtained, and confidence intervals were used to determine if there were differences between the patients and control. Correlations between participant and control mean joint waveforms were calculated and used to evaluate the similarities between patients and controls. Non-linear measures included: joint angle-angle diagrams, phase-portrait areas, and continuous relative phase (CRP) measures. These measures were used to assess joint coordination and control features of the lower limb motion. Participants displayed high correlations with their control counterparts for the hip and knee joint waveforms, but joint motion was restricted. Peak angular velocities were also significantly less than those of the controls. Both angle-angle and phase-portrait areas were less than the controls although the general shapes of those diagrams were similar to those of the controls. The NGLY1 Deficient participants’ CRP measures displayed disrupted coordination patterns with the knee-ankle patterns displaying more disruption than the hip-knee measures. Overall, the participants displayed a functional walking pattern that differed in many quantitative ways from those of the neurotypical controls. Using both linear and non-linear measures to characterize gait provides a more comprehensive and nuanced characterization of NGLY1 gait and can be used to develop interventions targeted toward specific aspects of disordered gait.
