Improved Vicsek model based on two exponential coupling functions

In order to speed up the consensus of the Vicsek model, existing studies assign different coupling strengths according to the inter-particle Euclidean distance, which effectively reduces the convergence step. In this paper, we propose two new coupling functions, resulting in two improved Vicsek models. Improved Model I introduces the exponential Relu coupling function into the original Vicsek model, and Improved Model II introduces the exponential Swish coupling function into the original Vicsek model. Simulations show that both improved Vicsek models have fewer convergence steps than the original improved Vicsek model based on the coupling function. With different system parameters, the number of convergence steps is smaller than the original improved Vicsek model based on the coupling function. In addition, the number of convergence steps further decreases when the exponent increases and then gradually remains constant. The improved Vicsek model II also achieves better results in resisting noise.