To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with differential Chay model, this paper fits a discontinuous map of a slow control va...To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with differential Chay model, this paper fits a discontinuous map of a slow control variable of Chay model based on simulation results. The procedure of period adding bifurcation scenario from period k to period k ＋ 1 bursting （k = 1, 2, 3, 4） involved in the period-adding cascades and the stochastic effect of noise near each bifurcation point is also reproduced in the discontinuous map. Moreover, dynamics of the border-collision bifurcation is identified in the discontinuous map, which is employed to understand the experimentally observed period increment sequence. The simple discontinuous map is of practical importance in modeling of collective behaviours of neural populations like synchronization in large neural circuits.展开更多
A model of double-harmonious circuit for non-feedback control of chaos is introduced. A controlling signal is added to the coefficient for two-order term of the nonlinear differential equation The effect of controllin...A model of double-harmonious circuit for non-feedback control of chaos is introduced. A controlling signal is added to the coefficient for two-order term of the nonlinear differential equation The effect of controlling signal on controlling chaos is studied. By changing the controlling frequency fk and controlling strength Ik, chaos to period-doubling, period-adding and quasi-period state can be controlled. The effect of phase on controlling chaos is also discussed. A breathing phenomenon is observed and its mechanism is explained.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10774088,10772101,30770701 and 10875076)the Fundamental Research Funds for the Central Universities(Grant No.GK200902025)
文摘To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with differential Chay model, this paper fits a discontinuous map of a slow control variable of Chay model based on simulation results. The procedure of period adding bifurcation scenario from period k to period k ＋ 1 bursting （k = 1, 2, 3, 4） involved in the period-adding cascades and the stochastic effect of noise near each bifurcation point is also reproduced in the discontinuous map. Moreover, dynamics of the border-collision bifurcation is identified in the discontinuous map, which is employed to understand the experimentally observed period increment sequence. The simple discontinuous map is of practical importance in modeling of collective behaviours of neural populations like synchronization in large neural circuits.
基金the National Natural Science Foundation of China
文摘A model of double-harmonious circuit for non-feedback control of chaos is introduced. A controlling signal is added to the coefficient for two-order term of the nonlinear differential equation The effect of controlling signal on controlling chaos is studied. By changing the controlling frequency fk and controlling strength Ik, chaos to period-doubling, period-adding and quasi-period state can be controlled. The effect of phase on controlling chaos is also discussed. A breathing phenomenon is observed and its mechanism is explained.
