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
This paper investigates the generation of complex bursting patterns in Van der Pol system with two slowly changing external forcings. Complex bursting patterns, including complex periodic bursting and chaotic bursting...This paper investigates the generation of complex bursting patterns in Van der Pol system with two slowly changing external forcings. Complex bursting patterns, including complex periodic bursting and chaotic bursting, are presented for the cases when the two frequencies are commensurate and incommensurate. These complex bursting patterns are novel and have not been reported in previous work. Based on the fast-slow dynamics, the evolution processes of the slow forcing are presented to reveal the dynamical mechanisms undedying the appearance of these complex bursting patterns. With the change of ampli- tudes and frequencies, the slow forcing may visit the spiking and rest areas in different ways, which leads to the generation of different complex bursting patterns.展开更多
The study of synchronization and bursting transition is very important and valuable in cognitive activities and action control of brain as well as enhancement for the reliability of the cortex synapses. However, we wo...The study of synchronization and bursting transition is very important and valuable in cognitive activities and action control of brain as well as enhancement for the reliability of the cortex synapses. However, we wonder how the synaptic strength and synaptic delay, especially the asymmetrical time-delays between different neurons can collectively influence their synchronous firing behaviors. In this paper, based on the Hindmarsh-Rose neuronal systems with asymmetrical time-delays, we investigate the collective effects of various delays and coupling strengths on the synchronization and bursting transition. It is shown that the interplay between delay and coupling strength can not only enhance or destroy the synchronizations but also can induce the regular transitions of bursting firing patterns. Specifically, as the coupling strength or time-delay increasing, the firing patterns of the time-delayed coupling neuronal systems consistently present a regular transition, that is, the periods of spikes during the bursting firings increase firstly and then decrease slowly. In particular, in contrast to the case of symmetrical time-delays,asymmetrical time-delays can lead to the paroxysmal synchronizations of coupling neuronal systems, as well as the concentration level of synchronization for the non-identically coupled system is superior to the one of identical coupling. These results more comprehensively reveal the rich nonlinear dynamical behaviors of neuronal systems and may be helpful for us to have a better understanding of the neural coding.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supported by the National Natural Science Foundation of China (Grant Nos. 10872080, 20976075, 10972091 and 11102076)the Research Foundation for Advanced Talents of Jiangsu University (Grant No. 11JDG075)the Natural Science Foundation of Higher Education Institutions of Jiangsu Province (Grant No. 10KJD110006)
文摘This paper investigates the generation of complex bursting patterns in Van der Pol system with two slowly changing external forcings. Complex bursting patterns, including complex periodic bursting and chaotic bursting, are presented for the cases when the two frequencies are commensurate and incommensurate. These complex bursting patterns are novel and have not been reported in previous work. Based on the fast-slow dynamics, the evolution processes of the slow forcing are presented to reveal the dynamical mechanisms undedying the appearance of these complex bursting patterns. With the change of ampli- tudes and frequencies, the slow forcing may visit the spiking and rest areas in different ways, which leads to the generation of different complex bursting patterns.
基金supported by the National Natural Science Foundation of China(Grant Nos.11325208&11572015)the Innovation Foundation of Beijing University of Aeronautics and Astronautics for PhD Graduates
文摘The study of synchronization and bursting transition is very important and valuable in cognitive activities and action control of brain as well as enhancement for the reliability of the cortex synapses. However, we wonder how the synaptic strength and synaptic delay, especially the asymmetrical time-delays between different neurons can collectively influence their synchronous firing behaviors. In this paper, based on the Hindmarsh-Rose neuronal systems with asymmetrical time-delays, we investigate the collective effects of various delays and coupling strengths on the synchronization and bursting transition. It is shown that the interplay between delay and coupling strength can not only enhance or destroy the synchronizations but also can induce the regular transitions of bursting firing patterns. Specifically, as the coupling strength or time-delay increasing, the firing patterns of the time-delayed coupling neuronal systems consistently present a regular transition, that is, the periods of spikes during the bursting firings increase firstly and then decrease slowly. In particular, in contrast to the case of symmetrical time-delays,asymmetrical time-delays can lead to the paroxysmal synchronizations of coupling neuronal systems, as well as the concentration level of synchronization for the non-identically coupled system is superior to the one of identical coupling. These results more comprehensively reveal the rich nonlinear dynamical behaviors of neuronal systems and may be helpful for us to have a better understanding of the neural coding.
