Network synchronization under periodic coupling of both positive and negative values

We revisit a system of networked chaotic oscillators subjected to a common periodic coupling, where the coupling is governed by constant coupling strength, coupling frequency, and coupling amplitude. Utilizing the method of master stability function, the effect of periodic coupling on network synchronization is analyzed in detail, and numerical results are verified. It is found that when the coupling is a mixture of both periodic positive and negative couplings, the performance of network synchronization is better than that of periodic positive coupling. Utilizing the approach of finite-time Lyapunov exponent, we find the mechanism for the maximized synchronization performance, that is, the power spectrum of the finite-time Lyapunov exponent, at the characteristic frequencies, is varied from local to wide distributions. If this feature is missing or less prominent, the periodic coupling has less effect on synchronization performance. Our study indicates the validity of the finite-time Lyapunov exponent approach in detecting the synchronization behavior of coupled oscillators and is helpful for grasping the collective behavior of networks with positive and negative couplings. Graphical abstract 1. Periodic coupling enables synchronization in an infinite range of the constant coupling strength by tuning the coupling frequency or the coupling amplitude (left panel). 2. The high frequency of periodic coupling can also achieve enhanced synchronization (right panel). 3. We use the FTLE approach to reveal the underlying mechanism of synchronization. It is found that the optimized synchronization is attributed to the drastic response of the FTLE approach to periodic coupling.