Dynamics of Rössler oscillators in a star network with the central node controlled by an external system

The present work studies the dynamics of chaotic Rossler 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.