Studies of sustained oscillations on complex networks with excitable node dynamics received much interest in recent years.Although an individual unit is non-oscillatory,they may organize to form various collective osc...Studies of sustained oscillations on complex networks with excitable node dynamics received much interest in recent years.Although an individual unit is non-oscillatory,they may organize to form various collective oscillatory patterns through networked connections.An excitable network usually possesses a number of oscillatory modes dominated by different Winfree loops and numerous spatiotemporal patterns organized by different propagation path distributions.The traditional approach of the so-called dominant phase-advanced drive method has been well applied to the study of stationary oscillation patterns on a network.In this paper,we develop the functional-weight approach that has been successfully used in studies of sustained oscillations in gene-regulated networks by an extension to the high-dimensional node dynamics.This approach can be well applied to the study of sustained oscillations in coupled excitable units.We tested this scheme for different networks,such as homogeneous random networks,small-world networks,and scale-free networks and found it can accurately dig out the oscillation source and the propagation path.The present approach is believed to have the potential in studies competitive non-stationary dynamics.展开更多
All dynamic complex networks have two important aspects, pattern dynamics and network topology. Discovering different types of pattern dynamics and exploring how these dynamics depend or/network topologies are tasks o...All dynamic complex networks have two important aspects, pattern dynamics and network topology. Discovering different types of pattern dynamics and exploring how these dynamics depend or/network topologies are tasks of both great theoretical importance and broad practical significance. In this paper we study the oscillatory behaviors of excitable complex networks （ECNs） and find some interesting dynamic behaviors of ECNs in oscillatory probability, the multiplicity of oscillatory attractors, period distribution, and different types of oscillatory patterns （e.g., periodic, quasiperiodic, and chaotic）. In these aspects, we further explore strikingly sharp differences among network dynamics induced by different topologies （random or scale-free topologies） and different interaction structures （symmetric or asymmetric couplings）. The mechanisms behind these differences are explained physically.展开更多
Synchronization rhythm and oscillating in biological systems can give clues to understanding the cooperation and competition between cells under appropriate biological and physical conditions. As a result, the network...Synchronization rhythm and oscillating in biological systems can give clues to understanding the cooperation and competition between cells under appropriate biological and physical conditions. As a result, the network setting is appreciated to detect the stability and transition of collective behaviors in a network with different connection types. In this paper, the synchronization performance in time-delayed excitable homogeneous random networks（EHRNs） induced by diversity in system parameters is investigated by calculating the synchronization parameter and plotting the spatiotemporal evolution pattern, and distinct impacts induced by parameter-diversity are detected by setting different time delays. It is found that diversity has no distinct effect on the synchronization performance in EHRNs with small time delay being considered. When time delay is increased greatly, the synchronization performance of EHRN degenerates remarkably as diversity is increased. Surprisingly, by setting a moderate time delay, appropriate parameter-diversity can promote the synchronization performance in EHRNs, and can induce the synchronization transition from the asynchronous state to the weak synchronization. Moreover, the bistability phenomenon, which contains the states of asynchronous state and weak synchronization,is observed. Particularly, it is confirmed that the parameter-diversity promoted synchronization performance in time-delayed EHRN is manifested in the enhancement of the synchronization performance of individual oscillation and the increase of the number of synchronization transitions from the asynchronous state to the weak synchronization. Finally, we have revealed that this kind of parameter-diversity promoted synchronization performance is a robust phenomenon.展开更多
The electrical excitability of neural networks is influenced by different environmental factors. Effective and simple methods are required to objectively and quantitatively evaluate the influence of such factors, incl...The electrical excitability of neural networks is influenced by different environmental factors. Effective and simple methods are required to objectively and quantitatively evaluate the influence of such factors, including variations in temperature and pharmaceutical dosage. The aim of this paper was to introduce ‘the voltage threshold measurement method＇, which is a new method using microelectrode arrays that can quantitatively evaluate the influence of different factors on the electrical excitability of neural networks. We sought to verify the feasibility and efficacy of the method by studying the effects of acetylcholine, ethanol, and temperature on hippocampal neuronal networks and hippocampal brain slices. First, we determined the voltage of the stimulation pulse signal that elicited action potentials in the two types of neural networks under normal conditions. Second, we obtained the voltage thresholds for the two types of neural networks under different concentrations of acetylcholine, ethanol, and different temperatures. Finally, we obtained the relationship between voltage threshold and the three influential factors. Our results indicated that the normal voltage thresholds of the hippocampal neuronal network and hippocampal slice preparation were 56 and 31 m V, respectively. The voltage thresholds of the two types of neural networks were inversely proportional to acetylcholine concentration, and had an exponential dependency on ethanol concentration. The curves of the voltage threshold and the temperature of the medium for the two types of neural networks were U-shaped. The hippocampal neuronal network and hippocampal slice preparations lost their excitability when the temperature of the medium decreased below 34 and 33°C or increased above 42 and 43°C, respectively. These results demonstrate that the voltage threshold measurement method is effective and simple for examining the performance/excitability of neuronal networks.展开更多
Spiral waves have been observed in the biological experiments on rat cortex perfused with drugs which can block inhibitory synapse and switch neuron excitability from type II to type I. To simulate the spiral waves ob...Spiral waves have been observed in the biological experiments on rat cortex perfused with drugs which can block inhibitory synapse and switch neuron excitability from type II to type I. To simulate the spiral waves observed in the experiment, the spatiotemporal patterns are investigated in a network composed of neurons with type I and II excitabilities and excitatory coupling. Spiral waves emerge when the percentage(p) of neurons with type I excitability in the network is at middle levels, which is dependent on the coupling strength. Compared with other spatial patterns which appear at different p values, spiral waves exhibit optimal spatial correlation at a certain spatial frequency, implying the occurrence of spatial coherence resonance-like phenomenon. Some dynamical characteristics of the network such as mean firing frequency and synchronous degree can be well interpreted with distinct properties between type I excitability and type II excitability. The results not only identify dynamics of spiral waves in neuronal networks composed of neurons with different excitabilities, but also are helpful to understanding the emergence of spiral waves observed in the biological experiment.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11875135).
文摘Studies of sustained oscillations on complex networks with excitable node dynamics received much interest in recent years.Although an individual unit is non-oscillatory,they may organize to form various collective oscillatory patterns through networked connections.An excitable network usually possesses a number of oscillatory modes dominated by different Winfree loops and numerous spatiotemporal patterns organized by different propagation path distributions.The traditional approach of the so-called dominant phase-advanced drive method has been well applied to the study of stationary oscillation patterns on a network.In this paper,we develop the functional-weight approach that has been successfully used in studies of sustained oscillations in gene-regulated networks by an extension to the high-dimensional node dynamics.This approach can be well applied to the study of sustained oscillations in coupled excitable units.We tested this scheme for different networks,such as homogeneous random networks,small-world networks,and scale-free networks and found it can accurately dig out the oscillation source and the propagation path.The present approach is believed to have the potential in studies competitive non-stationary dynamics.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11174034,11135001,11205041,and 11305112)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20130282)
文摘All dynamic complex networks have two important aspects, pattern dynamics and network topology. Discovering different types of pattern dynamics and exploring how these dynamics depend or/network topologies are tasks of both great theoretical importance and broad practical significance. In this paper we study the oscillatory behaviors of excitable complex networks （ECNs） and find some interesting dynamic behaviors of ECNs in oscillatory probability, the multiplicity of oscillatory attractors, period distribution, and different types of oscillatory patterns （e.g., periodic, quasiperiodic, and chaotic）. In these aspects, we further explore strikingly sharp differences among network dynamics induced by different topologies （random or scale-free topologies） and different interaction structures （symmetric or asymmetric couplings）. The mechanisms behind these differences are explained physically.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11675001,11675112,11775020,and 11372122)
文摘Synchronization rhythm and oscillating in biological systems can give clues to understanding the cooperation and competition between cells under appropriate biological and physical conditions. As a result, the network setting is appreciated to detect the stability and transition of collective behaviors in a network with different connection types. In this paper, the synchronization performance in time-delayed excitable homogeneous random networks（EHRNs） induced by diversity in system parameters is investigated by calculating the synchronization parameter and plotting the spatiotemporal evolution pattern, and distinct impacts induced by parameter-diversity are detected by setting different time delays. It is found that diversity has no distinct effect on the synchronization performance in EHRNs with small time delay being considered. When time delay is increased greatly, the synchronization performance of EHRN degenerates remarkably as diversity is increased. Surprisingly, by setting a moderate time delay, appropriate parameter-diversity can promote the synchronization performance in EHRNs, and can induce the synchronization transition from the asynchronous state to the weak synchronization. Moreover, the bistability phenomenon, which contains the states of asynchronous state and weak synchronization,is observed. Particularly, it is confirmed that the parameter-diversity promoted synchronization performance in time-delayed EHRN is manifested in the enhancement of the synchronization performance of individual oscillation and the increase of the number of synchronization transitions from the asynchronous state to the weak synchronization. Finally, we have revealed that this kind of parameter-diversity promoted synchronization performance is a robust phenomenon.
基金supported by the National Natural Sciences Foundation of China,No.61534003,61076118the Innovation Foundation for State Key Laboratory of the Ministry of Science and Technology,China,No.2016-2018a grant from the Open Projects of Key Laboratory of Child Development and Learning of the Ministry of Education of China,No.CDLS201205
文摘The electrical excitability of neural networks is influenced by different environmental factors. Effective and simple methods are required to objectively and quantitatively evaluate the influence of such factors, including variations in temperature and pharmaceutical dosage. The aim of this paper was to introduce ‘the voltage threshold measurement method＇, which is a new method using microelectrode arrays that can quantitatively evaluate the influence of different factors on the electrical excitability of neural networks. We sought to verify the feasibility and efficacy of the method by studying the effects of acetylcholine, ethanol, and temperature on hippocampal neuronal networks and hippocampal brain slices. First, we determined the voltage of the stimulation pulse signal that elicited action potentials in the two types of neural networks under normal conditions. Second, we obtained the voltage thresholds for the two types of neural networks under different concentrations of acetylcholine, ethanol, and different temperatures. Finally, we obtained the relationship between voltage threshold and the three influential factors. Our results indicated that the normal voltage thresholds of the hippocampal neuronal network and hippocampal slice preparation were 56 and 31 m V, respectively. The voltage thresholds of the two types of neural networks were inversely proportional to acetylcholine concentration, and had an exponential dependency on ethanol concentration. The curves of the voltage threshold and the temperature of the medium for the two types of neural networks were U-shaped. The hippocampal neuronal network and hippocampal slice preparations lost their excitability when the temperature of the medium decreased below 34 and 33°C or increased above 42 and 43°C, respectively. These results demonstrate that the voltage threshold measurement method is effective and simple for examining the performance/excitability of neuronal networks.
基金supported by the National Natural Science Foundation of China(Grant Nos.11372224&11572225)
文摘Spiral waves have been observed in the biological experiments on rat cortex perfused with drugs which can block inhibitory synapse and switch neuron excitability from type II to type I. To simulate the spiral waves observed in the experiment, the spatiotemporal patterns are investigated in a network composed of neurons with type I and II excitabilities and excitatory coupling. Spiral waves emerge when the percentage(p) of neurons with type I excitability in the network is at middle levels, which is dependent on the coupling strength. Compared with other spatial patterns which appear at different p values, spiral waves exhibit optimal spatial correlation at a certain spatial frequency, implying the occurrence of spatial coherence resonance-like phenomenon. Some dynamical characteristics of the network such as mean firing frequency and synchronous degree can be well interpreted with distinct properties between type I excitability and type II excitability. The results not only identify dynamics of spiral waves in neuronal networks composed of neurons with different excitabilities, but also are helpful to understanding the emergence of spiral waves observed in the biological experiment.
