In this study, the collective and stochastic resonance (SR) behavior of a stochastic nearest neighbor coupled system in a dichotomous fluctuating potential driven by a periodic force are investigated. The exact conditions of stability, synchronization and SR of the system are given analytically and verified by a numerical algorithm. We find that the final dynamic behaviors of the system are the results of the synergy of the coupled system, noise and external periodic force: the stationary regime criterion is only related to the noise parameters and system potential parameter; the synchronization criterion is related to the number of particles, coupling strength, noise parameters and system potential parameter. Furthermore, for the stationary regime, all particles synchronously move with their mean field and show SR phenomenon. For the non-stationary regime, the power-law distribution is observed when the synchronization criteria is satisfied.

在这项研究中，研究了由周期性力驱动的二分波动势中的随机最近邻居耦合系统的集体和随机共振（SR）行为。给出了系统的稳定性，同步性和SR的确切条件，并通过数值算法进行了验证。我们发现，系统的最终动态行为是耦合系统，噪声和外部周期性力协同作用的结果：平稳状态准则仅与噪声参数和系统电势参数有关；同步标准与粒子数，耦合强度，噪声参数和系统电势参数有关。此外，对于静止状态，所有粒子均与其平均场同步移动并显示SR现象。