Projective synchronisation of bipartite networks with nonlinear couplings via quantised event-triggered control

In this paper, the issue of projective synchronisation of bipartite networks (BNs) with multiple time-varying delays and nonlinear couplings has been studied. To reduce wasted communication resources, the novel quantised event-triggered controllers and the measurement error functions are introduced. In particular, the event-triggered schemes without Zeno behaviour are designed, which can determine whether controllers need to be updated or not. For the purpose of investigating the synchronisation with isolated nodes, comparing to the usual 1-norm and 2-norm, generalised $ \{\xi,1\} $ { xi , 1 } -norm has been utilised to derive sufficient conditions. Furthermore, in the proof of the theorem, constant time-delays and time-varying time delays are dealt with by utilising novel Lyapunov functions, and then some valid criteria are established to achieve different types of projective synchronisation. Lastly, numerical simulations are well provided to confirm the given theoretical results.