Synchronization State in the Coupled Van Der Pol Oscillators within a Small Invariant Subspace

This study aims to analyze the dynamics of trajectories in a system of Van der Pol with the coupled oscillator. The control parameters considered are damping and coupling strength. We focus on study the behaviour of this system within a specific small invariant subspace. It is used phase difference to reduce the dimension of this system into two dimensions. Then, the Jacobian matrix is computed eigenvalues in order to determine the stability of equilibrium point. this work specifically discovers the effects the damping and coupling strength parameters to emerge synchronization states. additionally, it investigates how change the value of damping parameter influence on the system's energy.