Different types of collective dynamical behavior of the coupled oscillator networks are investigated under heterogeneous environmental coupling. This type of interaction pattern mainly occurs indirectly between two or more dynamical units. By interplaying the diffusive and the environmental coupling, the transition scenarios among several collective states, such as complete synchronization, amplitude, and oscillation death are explored in the coupled dynamical network. Here we consider a heterogeneous environmental coupling scheme, meaning that two or more dynamical units are not only connected via one medium but they can rely on their information through more than one medium. Another type of heterogeneity is introduced in terms of the coupling asymmetry in the interacting network structure and it is observed that the proper tuning of the coupling heterogeneity parameter is capable of restoring the dynamic rhythm from the oscillation suppressed state. Using detailed bifurcation analysis it is shown that the asymmetry parameter plays a key role in the transition among the several collective dynamical states and we map them in the different parameter space. We analytically derived the stability conditions for the existence of different dynamical states. The analytical findings are confirmed by numerical results. We performed the numerical simulation on networks of Stuart-Landau oscillators. Finally, we extend this investigation to large network sizes. In this case, we observe the novel transitions from amplitude death to multicluster oscillation death states and correspondingly, the revival of oscillations from the different suppressed states is also articulated.

在异构环境耦合下研究了耦合振荡器网络的不同类型的集体动力学行为。这种类型的交互模式主要间接发生在两个或多个动力学单元之间。通过相互作用的扩散和环境耦合，在耦合的动力学网络中探索了几个集体状态之间的过渡情形，例如完全同步，振幅和振荡死亡。在这里，我们考虑一种异构的环境耦合方案，这意味着两个或多个动态单元不仅通过一种介质连接，而且可以通过一种以上的介质依赖其信息。根据相互作用网络结构中的耦合不对称性，引入了另一种类型的异质性，并且观察到，耦合异质性参数的适当调整能够从振荡抑制状态恢复动态节律。使用详细的分叉分析表明，不对称参数在几个集体动力学状态之间的转换中起着关键作用，我们将它们映射在不同的参数空间中。我们通过分析得出了存在不同动力学状态的稳定性条件。数值结果证实了分析结果。我们在Stuart-Landau振荡器的网络上进行了数值模拟。最后，我们将此调查扩展到大型网络。在这种情况下，