| For a long period of time, Human dynamics and Coupled limit-cycle oscillator networks have attracted wide attention as two parallel subjects in the world of science, and fruitful researches on them have been published. Although some scholars have noticed that periodicity is widely observed in the patterns Human activity, few investigated human dynamics from the aspect of limit-cycle oscillators. One reason for this lies in the lack of proper model, for traditionallymodelinghuman network is usually based on statistical information. Inspired by this, we tend to establish a coupled limit-cycle oscillator model, which can properly describe the fundamental feature of human interactions. Consequently, this model may not only provide a new method to understand human dynamics, but also widen the applications of coupled limit-cycle oscillator networks.In late1970s and early1980s, Japanese scholar, Kuramoto, proposed the famous Kuramoto Model to study the dynamics of coupled limit-cycle oscillators. The Kuramoto Model has been widely and deeply studied, and has found its applications in many areas since then. However, Kuramoto put too many simplifications on his model, neglecting some fundamental features of human interactions. Thus, we modified the Kuramoto model to a frequency-weighted one by adding the features of human interactions to it. We studied the dynamics of the new model both from the simulative and analytical aspects. Our simulations indicate that the model exhibits rich dynamics including incoherence, partially synchronization, synchronization, oscillatory and the so called Chimera states. Further, we give thorough explanation for its dynamics by reducing the N dimensional system to a4-dimension or less system and then analyzing its bifurcations. In the last part of this paper, we propose a method to control the dynamics of our model.This paper is initially inspired by the combination of human activity and limit-cycle oscillators. However, the core of it lies in the model itself, including modeling, bifurcation analysis and control. Our paper is innovative in following aspects:1. The model we proposed captures the inner feature of human interactions, thus may be applicable in future study of the periodicity of human activities.2. The model exhibitrich dynamics, especially the so called’Chimera States’, and our simulations and analysis make contribution on understanding the basis of this intriguing phenomenon.3. With the help of mathematical tools, this paper reduced a N-dimension system to a4or less dimension one, whose validity has been improved by our simulations. With the reduced system, we plotted the bifurcation graphs of the original model, which helps understand the inner mechanics of the rich dynamics we observed.4. The paper as a whole, including modeling, bifurcation analysis and control, forms a complete research framework. The results of it is helpful for not only future applications, but also extending researches on specific dynamical phenomenon. |
