The present work studies the dynamics of chaotic Rössler oscillators in a star network, where the central node or relay system is controlled by an external and similar system. Without the outer systems, the middle oscillator of the network is an amplified observer of the driver. Varying both amplification and coupling parameters leads the outer systems and the driver–relay to various behaviors. To perform the robustness of the synchronization between different blocks of our network, a certain amount of noise is introduced in all the external systems. This is done to deal with not only the noise amplitude but also the cumulative effects since the noise is introduced in all the outer systems. Later, a finite duration feedback (taken as a single interval) from the relay to the driver is considered to improve the synchronization domain between the driver and relay unit and to accelerate the coherent motion between outer systems. We analyze how synchronization works using the Hamiltonian formalism. We confirm our analysis through mathematical developments and numerical simulations.

本工作研究星网络中混沌Rössler振荡器的动力学，该星网络的中央节点或中继系统由外部和类似系统控制。没有外部系统，网络的中间振荡器就是驱动器的放大观测器。放大和耦合参数的变化都会导致外部系统和驱动继电器产生各种行为。为了执行网络不同模块之间同步的鲁棒性，在所有外部系统中都会引入一定量的噪声。这样做不仅可以处理噪声幅度，还可以处理累积影响，因为在所有外部系统中都引入了噪声。后来，从继电器到驱动器的有限持续时间反馈（以单个间隔为单位）被认为可以改善驱动器和继电器单元之间的同步域并加速外部系统之间的连贯运动。我们使用Hamiltonian形式主义分析同步的工作方式。我们通过数学发展和数值模拟来确认我们的分析。