The onset of dynamic activity is studied in heterogeneous populations of globally coupled units such that each unit is either excitable or oscillatory depending on its parameter. By varying the mean of the parameter distribution as well as coupling strength, we show that all or part of the populations studied have common features: similar phase diagrams, hysteresis near or at the onset of dynamic activity, and a fractional power law obeyed by an order parameter. A simplified model is proposed to explain these results.
Following a previous paper [Phys. Rev. E 88, 052907 (2013)], we study in detail the mechanism of aging transition in globally and diffusively coupled excitable and oscillatory units. Here two of the three models taken up in the earlier work are used, each composed of a large number of units with their bifurcation parameters forming a uniform distribution. The control parameters are the coupling strength and the average of the bifurcation parameters. The present work is mostly devoted to a region of the phase diagram near the aging transition boundary with the coupling strength greater than its critical value for the onset of bistability and hysteresis. The bifurcation structure of each system at the aging transition boundary is investigated theoretically as well as numerically. Moreover, we show that critical scaling laws of order parameters S and M used in the previous paper are different depending on which region of the coupling strength to be chosen.
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