|Simon Fraser Univ.
We present a kinetic version of the Watanabe-Strogatz (WS) transform for vector models in this paper. From the generalized WS-transform, we can reduce the kinetic vector model into an ODE system. We also obtain the cross-ratio type constant of motion functionals for kinetic vector models under suitable conditions. We present the sufficient and necessary conditions for the existence of the suggested constant of motion functionals. As an application of the constant of motion functional, we provide the instability of bipolar states of the kinetic swarm sphere model. We also provide the WS-transform and constant of motion functionals for non-identical kinetic vector models.