A constructive theorem is established for generalized synchronization (GS) related to C<SUP>1</SUP> diffeomorphic transformations of unidirectionally coupled dynamical arrays. The theorem provides some int...A constructive theorem is established for generalized synchronization (GS) related to C<SUP>1</SUP> diffeomorphic transformations of unidirectionally coupled dynamical arrays. The theorem provides some interpretations about the underlying mechanism of various GS phenomena in nature. As a direct application of the theorem, a chaos-based secure Internet communication scheme is proposed. Moreover, a cellular neural network (CNN) of Chen's chaotic circuits with GS property is designed and studied. Numerical simulation shows that this Chen's CNN has high security and is fast and reliable for secure Internet communications.展开更多
The phenomenon of activity synchronization in biological neural network is considered. Simulation of neurons dynamics in the 6-layer neural network with 110 elements in different regimes： regular spikes, chaotic spik...The phenomenon of activity synchronization in biological neural network is considered. Simulation of neurons dynamics in the 6-layer neural network with 110 elements in different regimes： regular spikes, chaotic spikes, regular and chaotic bursting, etc was performed. Izhykevich＇s phenomenological model that displays different types of activity inherent for real biological neurons was used for simulation. Space-time diagram for the entire network and raster plots for the whole structure and for each layer separately were built for visual inspection of neural network activity synchronization. Synchronization coefficients based on cross-correlation times of action potentials for all neurons pairs were calculated for the whole neural system and for each layer separately.展开更多
In this study,we have formulated the phase description of the neuronal oscillator with non-instantaneous synaptic inputs and external periodic stimulus by using the phase sensitivity function.By numerical simulation,w...In this study,we have formulated the phase description of the neuronal oscillator with non-instantaneous synaptic inputs and external periodic stimulus by using the phase sensitivity function.By numerical simulation,we have found that the phase of a neuronal oscillator undergoes periodic evolution or locked state,which is determined by the synaptic time constant.The synaptic time constant is also an important condition under which the global network is synchronized.When the synaptic time constant is relatively small,perfectly synchronized behavior quickly occurs in the neuronal population.As the synaptic time constant becomes slightly larger,periodic synchronization emerges in the neuronal population.However,synchronized activity in the neuronal population is lost for larger synaptic time constant.The external periodic stimulus can change the synchronization patterns in the neuronal population.With a weak low-frequency stimulus,the neuronal populations quick synchronized bursting;whereas a high-frequency stimulus can produce synchronized overlapping bursting.We have also found that neuronal oscillators with type-II phase response curves are more susceptible to synchronization than those with type-I phase response curves.展开更多
Synchronization is considered to be a crucial mechanism that maintains respiratory rhythm.For understanding the effect of electrical coupling on the transition of the firing patterns and synchronization,we coupled two...Synchronization is considered to be a crucial mechanism that maintains respiratory rhythm.For understanding the effect of electrical coupling on the transition of the firing patterns and synchronization,we coupled two inspiratory pacemaker neurons together,and studied various synchronous behaviors between them.We firstly compared the bifurcation diagrams between the coupled neurons and single neuron,and found that the coupled neurons had a more complicated bifurcation mode.By increasing the coupling strength,the regular variation of phase differences was illustrated so that asynchronous and some synchronous states could be observed.These synchronous states were also shown in detail by phase portraits and firing series.In addition,we explored the ranges of different synchronous states,which attributed to different ranges of membrane capacitance and coupling strength.展开更多
We find that the fractional-order Hindmarsh-Rose model neuron demonstrates various types of firing behavior as a function of the fractional order in this study.There exists a clear difference in the bifurcation diagra...We find that the fractional-order Hindmarsh-Rose model neuron demonstrates various types of firing behavior as a function of the fractional order in this study.There exists a clear difference in the bifurcation diagram between the fractional-order Hindmarsh-Rose model and the corresponding integer-order model even though the neuron undergoes a Hopf bifurcation to oscillation and then starts a period-doubling cascade to chaos with the decrease of the externally applied current.Interestingly,the discharge frequency of the fractional-order Hindmarsh-Rose model neuron is greater than that of the integer-order counterpart irrespective of whether the neuron exhibits periodic or chaotic firing.Then we demonstrate that the firing behavior of the fractional-order Hindmarsh-Rose model neuron has a higher complexity than that of the integer-order counterpart.Also,the synchronization phenomenon is investigated in the network of two electrically coupled fractional-order model neurons.We show that the synchronization rate increases as the fractional order decreases.展开更多
In this paper, by the help of evolutionary algorithm and using Hindmarsh-Rose （HR） neuron model, we investigate the effect of topology structures on synchronization transition between different states in coupled neu...In this paper, by the help of evolutionary algorithm and using Hindmarsh-Rose （HR） neuron model, we investigate the effect of topology structures on synchronization transition between different states in coupled neuron cells system. First, we build different coupling structure with N cells, and found the effect of synchronized transition contact not only closely with the topology of the system, but also with whether there exist the ring structures in the system. In particular, both the size and the number of rings have greater effects on such transition behavior. Secondly, we introduce synchronization error to qualitative analyze the effect of the topology structure. Phrthermore, by fitting the simulation results, we find that with the increment of the neurons number, there always exist the optimization structures which have the minimum number of connecting edges in the coupling systems. Above results show that the topology structures have a very crucial role on synchronization transition in coupled neuron system. Biological system may gradually acquire such efficient topology structures through the long-term evolution, thus the systems＇ information process may be optimized by this scheme.展开更多
In this paper, we study how adaptive coupling with time-periodic growth speed (TPGS) affects the spiking synchronization of weighted adaptive Newman-Watts Hodgkin-Huxley neuron networks with time delays. It is found t...In this paper, we study how adaptive coupling with time-periodic growth speed (TPGS) affects the spiking synchronization of weighted adaptive Newman-Watts Hodgkin-Huxley neuron networks with time delays. It is found that the neuronal spiking intermittently exhibits synchronization transitions between desynchronization and in-phase synchronization or anti-phase synchronization as TPGS amplitude or frequency is varied, showing multiple synchronization transitions. These transitions depend on the values of time delay and can occur only when time delay is close to those values that can induce synchronization transitions when the growth speed is fixed. These results show that the adaptive coupling with TPGS has great influence on the spiking synchronization of the neuronal networks and thus plays a crucial role in the information processing and transmission in neural systems.展开更多
Synchronization of neurons plays an important role in vision, movement and memory. However, many neurological disorders such as epilepsies, Parkinson disease and essen- tial tremor are related to excessive synchroniza...Synchronization of neurons plays an important role in vision, movement and memory. However, many neurological disorders such as epilepsies, Parkinson disease and essen- tial tremor are related to excessive synchronization of neurons. In the line of therapy, stimulations to these pathologically synchronized neurons should be capable of breaking synchrony. As the first step of designing an effective stimulation, we consider desynchro- nization problem of coupled limit-cycle oscillators ensemble. First, the desynchronization problem is redefined in a nonlinear output regulation framework. Then, we design an output regulator （stimulation） which forces limit-cycle oscillators to track exogenous sinusoidal references with different phases. The proposed stimulation is robust against variations of oscillators＇ frequencies. Mathematical analysis and simulation results reveal the efficiency of the proposed technique.展开更多
Synchronization behavior of an ensemble of unidirectionally coupled neurons with a constant input is investigated. Chemical synapses are considered for coupling. Each neuron is also considered to be exposed to a self-...Synchronization behavior of an ensemble of unidirectionally coupled neurons with a constant input is investigated. Chemical synapses are considered for coupling. Each neuron is also considered to be exposed to a self-delayed feedback. The synchronization phenomenon is analyzed by the error dynamics of the response trajectories of the system. The effect of various model parameters e.g. coupling strength, feedback gain and time delay, on synchronization is also investigated and a measure of synchrony is computed in each cases. It is shown that the synchronization is not only achieved by increasing the coupling strength, the system also required to have a suitable feedback gain and time delay for synchrony. Robustness of the parameters for synchrony is verified for larger systems.展开更多
文摘已有的帕金森神经网络模型并未包含基底神经回路中的所有神经核团.因此,在研究发病机理和寻找最佳深部脑刺激(deep brain stimulation,DBS)的刺激靶点时忽略了其他核团潜在的影响.本文根据基底神经回路结构,利用Hindmarsh-Rose(HR)神经元模型成功构建了完整的帕金森神经网络模型.三种不同外加刺激下的数值仿真结果表明,缺失黑质致密部(substantia nigra pars compacta,SNc)核团的帕金森神经网络会出现神经元高度同步行为和异常β振荡活动,符合目前公认的帕金森发病机理,从而验证了所提的模型的合理性.此外,受生物伦理、实验难度的影响,电子神经网络更适合帕金森DBS治疗方案研究,因此,本文以SNc核团为例在现场可编程逻辑门阵列(field programmable gate array,FPGA)平台上构建了不同外加刺激下的SNc核团数字电路.电路实验结果能完整呈现出与数值仿真一致的放电行为,表明了数字电路设计的正确性.本文所设计的电路占用较低的数字电路资源,为帕金森神经网络电路实现做好基础准备.
文摘A constructive theorem is established for generalized synchronization (GS) related to C<SUP>1</SUP> diffeomorphic transformations of unidirectionally coupled dynamical arrays. The theorem provides some interpretations about the underlying mechanism of various GS phenomena in nature. As a direct application of the theorem, a chaos-based secure Internet communication scheme is proposed. Moreover, a cellular neural network (CNN) of Chen's chaotic circuits with GS property is designed and studied. Numerical simulation shows that this Chen's CNN has high security and is fast and reliable for secure Internet communications.
文摘The phenomenon of activity synchronization in biological neural network is considered. Simulation of neurons dynamics in the 6-layer neural network with 110 elements in different regimes： regular spikes, chaotic spikes, regular and chaotic bursting, etc was performed. Izhykevich＇s phenomenological model that displays different types of activity inherent for real biological neurons was used for simulation. Space-time diagram for the entire network and raster plots for the whole structure and for each layer separately were built for visual inspection of neural network activity synchronization. Synchronization coefficients based on cross-correlation times of action potentials for all neurons pairs were calculated for the whole neural system and for each layer separately.
基金supported by the National Natural Science Foundation of China(Grant Nos.1123200511172086)
文摘In this study,we have formulated the phase description of the neuronal oscillator with non-instantaneous synaptic inputs and external periodic stimulus by using the phase sensitivity function.By numerical simulation,we have found that the phase of a neuronal oscillator undergoes periodic evolution or locked state,which is determined by the synaptic time constant.The synaptic time constant is also an important condition under which the global network is synchronized.When the synaptic time constant is relatively small,perfectly synchronized behavior quickly occurs in the neuronal population.As the synaptic time constant becomes slightly larger,periodic synchronization emerges in the neuronal population.However,synchronized activity in the neuronal population is lost for larger synaptic time constant.The external periodic stimulus can change the synchronization patterns in the neuronal population.With a weak low-frequency stimulus,the neuronal populations quick synchronized bursting;whereas a high-frequency stimulus can produce synchronized overlapping bursting.We have also found that neuronal oscillators with type-II phase response curves are more susceptible to synchronization than those with type-I phase response curves.
基金supported by the National Natural Science Foundation of China(Grant No.11172103)
文摘Synchronization is considered to be a crucial mechanism that maintains respiratory rhythm.For understanding the effect of electrical coupling on the transition of the firing patterns and synchronization,we coupled two inspiratory pacemaker neurons together,and studied various synchronous behaviors between them.We firstly compared the bifurcation diagrams between the coupled neurons and single neuron,and found that the coupled neurons had a more complicated bifurcation mode.By increasing the coupling strength,the regular variation of phase differences was illustrated so that asynchronous and some synchronous states could be observed.These synchronous states were also shown in detail by phase portraits and firing series.In addition,we explored the ranges of different synchronous states,which attributed to different ranges of membrane capacitance and coupling strength.
基金supported by the National Natural Science Foundation of China(Grant Nos.11272241and 10972170)
文摘We find that the fractional-order Hindmarsh-Rose model neuron demonstrates various types of firing behavior as a function of the fractional order in this study.There exists a clear difference in the bifurcation diagram between the fractional-order Hindmarsh-Rose model and the corresponding integer-order model even though the neuron undergoes a Hopf bifurcation to oscillation and then starts a period-doubling cascade to chaos with the decrease of the externally applied current.Interestingly,the discharge frequency of the fractional-order Hindmarsh-Rose model neuron is greater than that of the integer-order counterpart irrespective of whether the neuron exhibits periodic or chaotic firing.Then we demonstrate that the firing behavior of the fractional-order Hindmarsh-Rose model neuron has a higher complexity than that of the integer-order counterpart.Also,the synchronization phenomenon is investigated in the network of two electrically coupled fractional-order model neurons.We show that the synchronization rate increases as the fractional order decreases.
基金Supported by the National Natural Science,and Special Found for the Theoretical Physics of China under Grant Nos.11275186,21103002,11047017the Special Foundation of Education of Anhui Province for Excellent Young Scientists under Grant No.2011SQRL023
文摘In this paper, by the help of evolutionary algorithm and using Hindmarsh-Rose （HR） neuron model, we investigate the effect of topology structures on synchronization transition between different states in coupled neuron cells system. First, we build different coupling structure with N cells, and found the effect of synchronized transition contact not only closely with the topology of the system, but also with whether there exist the ring structures in the system. In particular, both the size and the number of rings have greater effects on such transition behavior. Secondly, we introduce synchronization error to qualitative analyze the effect of the topology structure. Phrthermore, by fitting the simulation results, we find that with the increment of the neurons number, there always exist the optimization structures which have the minimum number of connecting edges in the coupling systems. Above results show that the topology structures have a very crucial role on synchronization transition in coupled neuron system. Biological system may gradually acquire such efficient topology structures through the long-term evolution, thus the systems＇ information process may be optimized by this scheme.
基金financially supported by the Natural Science Foundation of Shandong Province of China (ZR2012AM013)
文摘In this paper, we study how adaptive coupling with time-periodic growth speed (TPGS) affects the spiking synchronization of weighted adaptive Newman-Watts Hodgkin-Huxley neuron networks with time delays. It is found that the neuronal spiking intermittently exhibits synchronization transitions between desynchronization and in-phase synchronization or anti-phase synchronization as TPGS amplitude or frequency is varied, showing multiple synchronization transitions. These transitions depend on the values of time delay and can occur only when time delay is close to those values that can induce synchronization transitions when the growth speed is fixed. These results show that the adaptive coupling with TPGS has great influence on the spiking synchronization of the neuronal networks and thus plays a crucial role in the information processing and transmission in neural systems.
文摘Synchronization of neurons plays an important role in vision, movement and memory. However, many neurological disorders such as epilepsies, Parkinson disease and essen- tial tremor are related to excessive synchronization of neurons. In the line of therapy, stimulations to these pathologically synchronized neurons should be capable of breaking synchrony. As the first step of designing an effective stimulation, we consider desynchro- nization problem of coupled limit-cycle oscillators ensemble. First, the desynchronization problem is redefined in a nonlinear output regulation framework. Then, we design an output regulator （stimulation） which forces limit-cycle oscillators to track exogenous sinusoidal references with different phases. The proposed stimulation is robust against variations of oscillators＇ frequencies. Mathematical analysis and simulation results reveal the efficiency of the proposed technique.
文摘Synchronization behavior of an ensemble of unidirectionally coupled neurons with a constant input is investigated. Chemical synapses are considered for coupling. Each neuron is also considered to be exposed to a self-delayed feedback. The synchronization phenomenon is analyzed by the error dynamics of the response trajectories of the system. The effect of various model parameters e.g. coupling strength, feedback gain and time delay, on synchronization is also investigated and a measure of synchrony is computed in each cases. It is shown that the synchronization is not only achieved by increasing the coupling strength, the system also required to have a suitable feedback gain and time delay for synchrony. Robustness of the parameters for synchrony is verified for larger systems.
