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
The dynamics and the transition of spiral waves in the coupled Hindmarsh-Rose （H-R） neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in th...The dynamics and the transition of spiral waves in the coupled Hindmarsh-Rose （H-R） neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D＇, is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons （or sites） and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.展开更多
Chaos synchronization in an array of coupled chaotic neurons with symmetric coupling is investigated. A criterion for the stability of the synchronization manifold is deduced by transforming the variational equation o...Chaos synchronization in an array of coupled chaotic neurons with symmetric coupling is investigated. A criterion for the stability of the synchronization manifold is deduced by transforming the variational equation of the coupled system into a block diagonal one, and the critical coupling strengths for synchronization in different coupled cases are given. As examples for illustration, the HR neurons with the open-ended （i.e. chain）, ring, star and all-to-all （i.e. global） coupling schemes are considered. It is shown that the coupling scheme plays an important role in synchronization and information transmission of neurons.展开更多
In this paper, we investigate coherence resonance （CR） and noise-induced synchronization in Hindmarsh- Rose （HR） neural network with three different types of topologies： regular, random, and small-world. It is fo...In this paper, we investigate coherence resonance （CR） and noise-induced synchronization in Hindmarsh- Rose （HR） neural network with three different types of topologies： regular, random, and small-world. It is found that the additive noise can induce CR in HR neural network with different topologies and its coherence is optimized by a proper noise level. It is also found that as coupling strength increases the plateau in the measure of coherence curve becomes broadened and the effects of network topology is more pronounced simultaneously. Moreover, we find that increasing the probability p of the network topology leads to an enhancement of noise-induced synchronization in HR neurons network.展开更多
Spiral wave could be observed in the excitable media, the neurons are often excitable within appropriateparameters. The appearance and formation of spiral wave in the cardiac tissue is linked to monomorphic ventricula...Spiral wave could be observed in the excitable media, the neurons are often excitable within appropriateparameters. The appearance and formation of spiral wave in the cardiac tissue is linked to monomorphic ventriculartachycardia that can denervate into polymorphic tachycardia and ventricular fibrillation. The neuronal system oftenconsists of a large number of neurons with complex connections. In this paper, we theoretically study the transitionfrom spiral wave to spiral turbulence and homogeneous state (death of spiral wave) in two-dimensional array of theHindmarsh-Rose neuron with completely nearest-neighbor connections. In our numerical studies, a stable rotating spiralwave is developed and selected as the initial state, then the bifurcation parameters are changed to different values toobserve the transition from spiral wave to homogeneous state, breakup of spiral wave and weak change of spiral wave,respectively. A statistical factor of synchronization is defined with the mean field theory to analyze the transition fromspiral wave to other spatial states, and the snapshots of the membrane potentials of all neurons and time series of meanmembrane potentials of all neurons are also plotted to discuss the change of spiral wave. It is found that the sharpchanging points in the curve for factor of synchronization vs. bifurcation parameter indicate sudden transition fromspiral wave to other states. And the results are independent of the number of neurons we used.展开更多
A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh-Rose （HR） neuron model in many recent studies, which can interpret almost all of the previously simula...A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh-Rose （HR） neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two- dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the determin- istic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in dif- ferent two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.展开更多
Objective The relationship between compressed dorsal root ganglion （DRG） neurons and firing pattern and sensitivity of neurons was studied in chronically the Hindmarsh-Rose （HR） neuronal model. Methods Spontane- o...Objective The relationship between compressed dorsal root ganglion （DRG） neurons and firing pattern and sensitivity of neurons was studied in chronically the Hindmarsh-Rose （HR） neuronal model. Methods Spontane- ous activities from single fibers of chronically compressed DRG neurons in rats were recorded, and divided into periodic and non-periodic firing patterns. The sensitivity of the two kinds of firing pattern neuron to sympathetic stimulation （SS） was compared. Result It was found that 27.3% of periodic firing neurons and 93.2% of non-periodic firing neurons responded to SS respectively （ periodic vs non-periodic, P 〈 0.01 ）. The responses to SS with different stimulation time were greater non-periodic firing neurons than periodic firing neurons （P 〈 0.01 ）. The non-periodic firing neurons obviously responded to SS. After the firing pattern of these neurons transformed to periodic firing pattern, their responses to SS disappeared or decreased obviously. The HR neuronal model exhibited a significantly greater response to perturbation in non-periodic （chaotic） firing pattern than in periodic firing pattern. Conelusion The non-periodic firing neurons with deterministic chaos are more sensitive to external stimuli than the periodic firing neurons.展开更多
Due to the inherent insecure nature of the Internet,it is crucial to ensure the secure transmission of image data over this network.Additionally,given the limitations of computers,it becomes evenmore important to empl...Due to the inherent insecure nature of the Internet,it is crucial to ensure the secure transmission of image data over this network.Additionally,given the limitations of computers,it becomes evenmore important to employ efficient and fast image encryption techniques.While 1D chaotic maps offer a practical approach to real-time image encryption,their limited flexibility and increased vulnerability restrict their practical application.In this research,we have utilized a 3DHindmarsh-Rosemodel to construct a secure cryptosystem.The randomness of the chaotic map is assessed through standard analysis.The proposed system enhances security by incorporating an increased number of system parameters and a wide range of chaotic parameters,as well as ensuring a uniformdistribution of chaotic signals across the entire value space.Additionally,a fast image encryption technique utilizing the new chaotic system is proposed.The novelty of the approach is confirmed through time complexity analysis.To further strengthen the resistance against cryptanalysis attacks and differential attacks,the SHA-256 algorithm is employed for secure key generation.Experimental results through a number of parameters demonstrate the strong cryptographic performance of the proposed image encryption approach,highlighting its exceptional suitability for secure communication.Moreover,the security of the proposed scheme has been compared with stateof-the-art image encryption schemes,and all comparison metrics indicate the superior performance of the proposed scheme.展开更多
The effect of realistic topology configuration of intercellular connections on the response ability in coupled cell system is numerically investigated by using the Hindmarsh-Rose model. For the proper coupling intensi...The effect of realistic topology configuration of intercellular connections on the response ability in coupled cell system is numerically investigated by using the Hindmarsh-Rose model. For the proper coupling intensity, we set the control parameter to be near the critical value, and the external stimulus is introduced to the first cell in coupled system. It is found that, on one hand, when the cells are coupled with some proper topological structures, the external stimulus could transmit through the system, and shows better response ability and higher sensitivity. On the other hand, the influence of topological configuration on the synchronous ability and selection effect of neural system are also discussed. Our results display that the topology of coupled system may play an important role in the process of signal propagation, which could help us to understand the coordinated performance of cells in tissue.展开更多
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Project supported by the National Natural Science Foundation of China (Grant Nos 10747005,10572056 and 10774130)the Natural Science Foundation of Lanzhou University,China (Grant No Q200706)
文摘The dynamics and the transition of spiral waves in the coupled Hindmarsh-Rose （H-R） neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D＇, is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons （or sites） and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.
基金Supported by the National Natural Science Foundation of China under Grant No 10432010.
文摘Chaos synchronization in an array of coupled chaotic neurons with symmetric coupling is investigated. A criterion for the stability of the synchronization manifold is deduced by transforming the variational equation of the coupled system into a block diagonal one, and the critical coupling strengths for synchronization in different coupled cases are given. As examples for illustration, the HR neurons with the open-ended （i.e. chain）, ring, star and all-to-all （i.e. global） coupling schemes are considered. It is shown that the coupling scheme plays an important role in synchronization and information transmission of neurons.
基金The project supported by National Natural Science Foundation of China under Grant No. 70571017
文摘In this paper, we investigate coherence resonance （CR） and noise-induced synchronization in Hindmarsh- Rose （HR） neural network with three different types of topologies： regular, random, and small-world. It is found that the additive noise can induce CR in HR neural network with different topologies and its coherence is optimized by a proper noise level. It is also found that as coupling strength increases the plateau in the measure of coherence curve becomes broadened and the effects of network topology is more pronounced simultaneously. Moreover, we find that increasing the probability p of the network topology leads to an enhancement of noise-induced synchronization in HR neurons network.
基金Supported by National Nature Science of Foundation of China under Grant Nos. 10747005, 10847140the Natural Science of Lanzhou University of Technology under Grant No. Q200706
文摘Spiral wave could be observed in the excitable media, the neurons are often excitable within appropriateparameters. The appearance and formation of spiral wave in the cardiac tissue is linked to monomorphic ventriculartachycardia that can denervate into polymorphic tachycardia and ventricular fibrillation. The neuronal system oftenconsists of a large number of neurons with complex connections. In this paper, we theoretically study the transitionfrom spiral wave to spiral turbulence and homogeneous state (death of spiral wave) in two-dimensional array of theHindmarsh-Rose neuron with completely nearest-neighbor connections. In our numerical studies, a stable rotating spiralwave is developed and selected as the initial state, then the bifurcation parameters are changed to different values toobserve the transition from spiral wave to homogeneous state, breakup of spiral wave and weak change of spiral wave,respectively. A statistical factor of synchronization is defined with the mean field theory to analyze the transition fromspiral wave to other spatial states, and the snapshots of the membrane potentials of all neurons and time series of meanmembrane potentials of all neurons are also plotted to discuss the change of spiral wave. It is found that the sharpchanging points in the curve for factor of synchronization vs. bifurcation parameter indicate sudden transition fromspiral wave to other states. And the results are independent of the number of neurons we used.
基金Project supported by the National Natural Science Foundation of China(Grant No.11072135)
文摘A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh-Rose （HR） neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two- dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the determin- istic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in dif- ferent two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.
基金This work was supported by the National Natural Science Foundation of China （30030040）.
文摘Objective The relationship between compressed dorsal root ganglion （DRG） neurons and firing pattern and sensitivity of neurons was studied in chronically the Hindmarsh-Rose （HR） neuronal model. Methods Spontane- ous activities from single fibers of chronically compressed DRG neurons in rats were recorded, and divided into periodic and non-periodic firing patterns. The sensitivity of the two kinds of firing pattern neuron to sympathetic stimulation （SS） was compared. Result It was found that 27.3% of periodic firing neurons and 93.2% of non-periodic firing neurons responded to SS respectively （ periodic vs non-periodic, P 〈 0.01 ）. The responses to SS with different stimulation time were greater non-periodic firing neurons than periodic firing neurons （P 〈 0.01 ）. The non-periodic firing neurons obviously responded to SS. After the firing pattern of these neurons transformed to periodic firing pattern, their responses to SS disappeared or decreased obviously. The HR neuronal model exhibited a significantly greater response to perturbation in non-periodic （chaotic） firing pattern than in periodic firing pattern. Conelusion The non-periodic firing neurons with deterministic chaos are more sensitive to external stimuli than the periodic firing neurons.
基金the Deanship of Scientific Research at Najran University for funding this work under the Research Groups Funding Program Grant Code(NU/RG/SERC/12/3).
文摘Due to the inherent insecure nature of the Internet,it is crucial to ensure the secure transmission of image data over this network.Additionally,given the limitations of computers,it becomes evenmore important to employ efficient and fast image encryption techniques.While 1D chaotic maps offer a practical approach to real-time image encryption,their limited flexibility and increased vulnerability restrict their practical application.In this research,we have utilized a 3DHindmarsh-Rosemodel to construct a secure cryptosystem.The randomness of the chaotic map is assessed through standard analysis.The proposed system enhances security by incorporating an increased number of system parameters and a wide range of chaotic parameters,as well as ensuring a uniformdistribution of chaotic signals across the entire value space.Additionally,a fast image encryption technique utilizing the new chaotic system is proposed.The novelty of the approach is confirmed through time complexity analysis.To further strengthen the resistance against cryptanalysis attacks and differential attacks,the SHA-256 algorithm is employed for secure key generation.Experimental results through a number of parameters demonstrate the strong cryptographic performance of the proposed image encryption approach,highlighting its exceptional suitability for secure communication.Moreover,the security of the proposed scheme has been compared with stateof-the-art image encryption schemes,and all comparison metrics indicate the superior performance of the proposed scheme.
文摘The effect of realistic topology configuration of intercellular connections on the response ability in coupled cell system is numerically investigated by using the Hindmarsh-Rose model. For the proper coupling intensity, we set the control parameter to be near the critical value, and the external stimulus is introduced to the first cell in coupled system. It is found that, on one hand, when the cells are coupled with some proper topological structures, the external stimulus could transmit through the system, and shows better response ability and higher sensitivity. On the other hand, the influence of topological configuration on the synchronous ability and selection effect of neural system are also discussed. Our results display that the topology of coupled system may play an important role in the process of signal propagation, which could help us to understand the coordinated performance of cells in tissue.
