Abstract
In this paper, we investigate synchronous solutions of coupled van der Pol oscillator systems with multiple coupling modes using the theory of rotating periodic solutions. Multiple coupling modes refer to two or three types of coupling modes in van der Pol oscillator networks, namely, position, velocity, and acceleration. Rotating periodic solutions can represent various types of synchronous solutions corresponding to different phase differences of coupled oscillators. When matrices representing the topology of different coupling modes have symmetry, the overall symmetry of the oscillator system depends on the intersection of the symmetries of the different topologies, determining the type of synchronous solutions for the coupled oscillator network. When matrices representing the topology of different coupling modes lack symmetry, if the adjacency matrices representing different coupling modes can be simplified into structurally identical quotient graphs (where weights can be proportional) through the same external equitable partition, the symmetry of the quotient graph determines the synchronization type of the original system. All these results are consistent with multi-layer networks where connections between different layers are one-to-one.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
