Coupled and Synchronization Models of Rhythmic Arm Movement in Planar Plane

Area of Science:

• Biomechanics
• Nonlinear Dynamics
• Robotics

Background:

• Nonlinear dynamics offer a novel framework for understanding human movement variability.
• The presence of chaotic behavior during rhythmic movements remains a subject of ongoing debate.

Purpose of the Study:

• To investigate the nonlinear dynamical behavior of coupled and synchronization models for planar rhythmic arm movements.
• To explore the potential for chaotic dynamics in human motor control.

Main Methods:

• Two coupling schemes were implemented between a planar arm model and an extended Duffing-Van der Pol (DVP) oscillator.
• Chaos analysis tools, including phase space, Poincaré sections, and Lyapunov exponents (LE), were employed.
• Synchronization was modeled using a Proportional Derivative (PD) scheme with the arm's orientation angle as a single-well DVP oscillator.

Main Results:

• The coupled system demonstrated rich dynamical behaviors, including periodic, quasi-periodic, and chaotic orbits.
• An advanced coupling scheme was identified as crucial for achieving a route to chaos.
• Synchronization between the arm's orientation and the drive system was successfully achieved via the PD-scheme.

Conclusions:

• Coupled nonlinear oscillator models can effectively represent complex dynamics in rhythmic arm movements.
• Chaotic dynamics are plausible in rhythmic movements, contingent on the coupling scheme.
• PD-controlled synchronization offers a viable method for coordinating movement dynamics.