Canonic coupling of oscillators in a chain (Q1093603)

The phenomenon of coupling of several sinusoidal oscillators is discussed. The oscillators are arranged in a chain, and each oscillator affects its next neighbour in the chain and is affected by it. The coupling is, therefore, bilateral and its main effect is due to variations in phase differences between neighbouring oscillators. The simple approach to the treatment of the behaviour of the coupling and the relative simplicity of the models of oscillators participating in the system enables an analytical solution to be found for many of the details of system dynamics without a need to resort to complicated approximate methods. The results are supported by computer simulation. The present work follows a previous successful treatment of simpler systems (a system of two coupled oscillators and a system of oscillators coupled in a ring). The paper concludes by considering the possible application of the present results for analysing some technological and natural systems.