Effects of amplitude dynamics for nonlinear coupled oscillator arrays

In this work, we seek to investigate the effects of amplitude dynamics, which were ignored in the analysis of previous works. A flowchart for implementing the full system dynamics is presented. Since the effects of amplitude dynamics are included, amplitudes of array elements will couple with the phases and also be varying over time. For both weak and strong coupling, the array factors are computed from the steady state phases and amplitudes. It is demonstrated that amplitude dynamics have significant effects upon the main beam scanning angle, and render control of the side lobe level with triangular amplitude distribution more difficult. However when the free-running amplitudes are identical for every element, main beam error is only 6% of the scanning angle with effects of the amplitude dynamics included.