Chiral magnetic vortex has shown great potential for high-density magnetic storage, modern telecommunication and computation devices, thanks to its topological stability and rich dynamic behaviours. Particularly, the synchronization of magnetic vortex nano-oscillators leads to the emergence of fascinating collective phenomena used for microwave generator and neuromorphic computing. In this work, by means of micromagnetic simulations, we create stable chiral magnetic vortices by exploiting the chiral coupling principle and study the gyrotropic motion of the vortex core under spin-transfer torques. The gyrotropic oscillation frequency can be tuned by injecting spin-polarised current as well as the change of the magnetic anisotropy in the vortex area, resulting from the modification of the vortex confine potential and the size of the vortex core. Two vortex nano-oscillators can be synchronized wherein the synchronization state can be modulated by the spin-polarised current and the magnetic anisotropy. Moreover, we demonstrate that the magnetic anisotropy can modify the synchronization patterns when integrating six vortices into an oscillator network, making it potentially serve as an oscillator-based neural network. Our work provides a new route to constructing a flexible oscillator network for neuromorphic computing hardware.