From collective rhythm to adaptive synchronization

A novel viewpoint, i.e., adaptive synchronization, is proposed to explore collective rhythm observed in many complex, self-organizing systems. We show that a simple adaptive coupling is able to tip arrays of oscillators towards collective synchronization. Two arrays of simply coupled Hindmarsh-Rose chaotic neurons are used to illustrate cooperative dynamics of neural activity like the central pattern generators, which supplies a new idea for biological experiments and numerical simulations. The results enhance the viewpoint that chaos is a necessary ingredient in life, and indicate that such small-world adaptive coupling may be a universal essence of the collective rhythm observed in nature.