Adaptive synchronisation of small-world networks with Lorenz chaotic oscillators

Synchronisation issues are important subjects in studying the dynamical performance of small-world networks. The backgrounds of the Lorenz system are given in details, and an adaptive synchronisation method is introduced to the small-world networks with Lorenz chaotic oscillators. The network achieves synchronisation asymptotically through adjusting the coupling strength according to a certain adaptive law, without requiring additional conditions for coupling matrix like the existing works. The numerical examples are applied to demonstrate and verify the effectiveness of the proposed method. The comparisons of the simulation results show that the new method appreciably reduces the synchronisation errors and increases the convergence speed to a certain extent.