A nonlinear model to generate the winner-take-all competition

This paper is concerned with the phenomenon of winner-take-all competition. In this paper, we propose a continuous-time dynamic model, which is described by an ordinary differential equation and is able to produce the winner-take-all competition by taking advantage of selective positive–negative feedback. The global convergence is proven analytically and the convergence rate is also discussed. Simulations are conducted in the static competition and the dynamic competition scenarios. Both theoretical and numerical results validate the effectiveness of the dynamic equation in describing the nonlinear phenomena of winner-take-all competition.

► The model has a simple dynamic.
► The convergence is rigorously proven.
► This model explains some winner-take-all phenomena in nature and society.