Nearest neighbour coupling for synchronization of coupled nonlinear systems

All-to-all coupling strategy for synchronization purposes is "expensive" and not practical, whereas nearest-neighbor coupling is more feasible. This paper proposes a systematic coupling strategy for synchronizing multiple nonlinear dynamical systems under the nearest-neighbor coupling category. The threshold value (i.e. the minimum value) of the coupling strength that can make coupled nonlinear system synchronize is also determined by setting the first oscillator as a reference and comparing the second and third oscillators with the first reference oscillator. A set of first-order and second-order coupled nonlinear oscillators are analyzed in terms of synchronization under the proposed coupling approach. It is shown that the coupling approach for synchronizing the systems depends on the order of the systems. Numerical simulations are conducted to verify the above analysis and compare the proposed coupling approach with the all-to-all coupling.