The human brain is a complex intelligent system composed of tens of billions of neurons interconnected through synapses,and its intricate network structure has consistently attracted numerous scientists to explore the...The human brain is a complex intelligent system composed of tens of billions of neurons interconnected through synapses,and its intricate network structure has consistently attracted numerous scientists to explore the mysteries of brain functions.However,most existing studies have only verified the biological mimicry characteristics of memristors at the single neuron-synapse level,and there is still a lack of research on memristors simulating synaptic coupling between neurons in multi-neuron networks.Based on this,this paper uses discrete memristors to couple dual discrete Rulkov neurons,and adds synaptic crosstalk between the two discrete memristors to form a neuronal network.A memristor-coupled dual-neuron map,called the Rulkov-memristor-Rulkov(R-M-R)map,is constructed to simulate synaptic connections between neurons in biological tissues.Then,the equilibrium points of the R-M-R map are studied.Subsequently,the effect of parameter variations on the dynamic performance of the R-M-R map is comprehensively analyzed using bifurcation diagram,phase diagram,Lyapunov exponent spectrum(LEs),firing diagram,and spectral entropy(SE)complexity algorithms.In the RM-R map,diverse categories of periodic,chaotic,and hyperchaotic attractors,as well as different states of firing patterns,can be observed.Additionally,different types of state transitions and coexisting attractors are discovered.Finally,the feasibility of the model in digital circuits is verified using a DSP hardware platform.In this study,the coupling principle of biological neurons is simulated,the chaotic dynamic behavior of the R-M-R map is analyzed,and a foundation is laid for deciphering the complex working mechanisms of the brain.展开更多
Based on the two-dimensional(2D)discrete Rulkov model that is used to describe neuron dynamics,this paper presents a continuous non-autonomous memristive Rulkov model.The effects of electromagnetic induction and exter...Based on the two-dimensional(2D)discrete Rulkov model that is used to describe neuron dynamics,this paper presents a continuous non-autonomous memristive Rulkov model.The effects of electromagnetic induction and external stimulus are simultaneously considered herein.The electromagnetic induction flow is imitated by the generated current from a flux-controlled memristor and the external stimulus is injected using a sinusoidal current.Thus,the presented model possesses a line equilibrium set evolving over the time.The equilibrium set and their stability distributions are numerically simulated and qualitatively analyzed.Afterwards,numerical simulations are executed to explore the dynamical behaviors associated to the electromagnetic induction,external stimulus,and initial conditions.Interestingly,the initial conditions dependent extreme multistability is elaborately disclosed in the continuous non-autonomous memristive Rulkov model.Furthermore,an analog circuit of the proposed model is implemented,upon which the hardware experiment is executed to verify the numerically simulated extreme multistability.The extreme multistability is numerically revealed and experimentally confirmed in this paper,which can widen the future engineering employment of the Rulkov model.展开更多
The exploration of the memristor model in the discrete domain is a fascinating hotspot.The electromagnetic induction on neurons has also begun to be simulated by some discrete memristors.However,most of the current in...The exploration of the memristor model in the discrete domain is a fascinating hotspot.The electromagnetic induction on neurons has also begun to be simulated by some discrete memristors.However,most of the current investigations are based on the integer-order discrete memristor,and there are relatively few studies on the form of fractional order.In this paper,a new fractional-order discrete memristor model with prominent nonlinearity is constructed based on the Caputo fractional-order difference operator.Furthermore,the dynamical behaviors of the Rulkov neuron under electromagnetic radiation are simulated by introducing the proposed discrete memristor.The integer-order and fractional-order peculiarities of the system are analyzed through the bifurcation graph,the Lyapunov exponential spectrum,and the iterative graph.The results demonstrate that the fractional-order system has more abundant dynamics than the integer one,such as hyper-chaos,multi-stable and transient chaos.In addition,the complexity of the system in the fractional form is evaluated by the means of the spectral entropy complexity algorithm and consequences show that it is affected by the order of the fractional system.The feature of fractional difference lays the foundation for further research and application of the discrete memristor and the neuron map in the future.展开更多
This article proposes a novel fractional heterogeneous neural network by coupling a Rulkov neuron with a Hopfield neural network(FRHNN),utilizing memristors for emulating neural synapses.The study firstly demonstrates...This article proposes a novel fractional heterogeneous neural network by coupling a Rulkov neuron with a Hopfield neural network(FRHNN),utilizing memristors for emulating neural synapses.The study firstly demonstrates the coexistence of multiple firing patterns through phase diagrams,Lyapunov exponents(LEs),and bifurcation diagrams.Secondly,the parameter related firing behaviors are described through two-parameter bifurcation diagrams.Subsequently,local attraction basins reveal multi-stability phenomena related to initial values.Moreover,the proposed model is implemented on a microcomputer-based ARM platform,and the experimental results correspond to the numerical simulations.Finally,the article explores the application of digital watermarking for medical images,illustrating its features of excellent imperceptibility,extensive key space,and robustness against attacks including noise and cropping.展开更多
At present, many neuron models have been proposed, which can be divided into discrete neuron models and continuous neuron models. Discrete neuron models have the advantage of faster simulation speed and the ease of un...At present, many neuron models have been proposed, which can be divided into discrete neuron models and continuous neuron models. Discrete neuron models have the advantage of faster simulation speed and the ease of understanding complex dynamic phenomena. Due to the properties of memorability, nonvolatility, and local activity, locally active discrete memristors(LADMs) are also suitable for simulating synapses. In this paper, we use an LADM to mimic synapses and establish a Rulkov neural network model. It is found that the change of coupling strength and the initial state of the LADM leads to multiple firing patterns of the neural network. In addition, considering the influence of neural network parameters and the initial state of the LADM, numerical analysis methods such as phase diagram and timing diagram are used to study the phase synchronization. As the system parameters and the initial states of the LADM change, the LADM coupled Rulkov neural network exhibits synchronization transition and synchronization coexistence.展开更多
The brain is a complex network system in which a large number of neurons are widely connected to each other and transmit signals to each other.The memory characteristic of memristors makes them suitable for simulating...The brain is a complex network system in which a large number of neurons are widely connected to each other and transmit signals to each other.The memory characteristic of memristors makes them suitable for simulating neuronal synapses with plasticity.In this paper,a memristor is used to simulate a synapse,a discrete small-world neuronal network is constructed based on Rulkov neurons and its dynamical behavior is explored.We explore the influence of system parameters on the dynamical behaviors of the discrete small-world network,and the system shows a variety of firing patterns such as spiking firing and triangular burst firing when the neuronal parameterαis changed.The results of a numerical simulation based on Matlab show that the network topology can affect the synchronous firing behavior of the neuronal network,and the higher the reconnection probability and number of the nearest neurons,the more significant the synchronization state of the neurons.In addition,by increasing the coupling strength of memristor synapses,synchronization performance is promoted.The results of this paper can boost research into complex neuronal networks coupled with memristor synapses and further promote the development of neuroscience.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.62571079)the Technological Innovation Projects in the Field of Artificial Intelligence in Liaoning Province(Grant No.2023JH26/10300011)+1 种基金the Basic Scientific Research Projects in the Department of Education of Liaoning Province(Grant No.LJ212410152049)the Liaoning Provincial Science and Technology Plan Joint Project(Grant No.2025-BSLH-041)。
文摘The human brain is a complex intelligent system composed of tens of billions of neurons interconnected through synapses,and its intricate network structure has consistently attracted numerous scientists to explore the mysteries of brain functions.However,most existing studies have only verified the biological mimicry characteristics of memristors at the single neuron-synapse level,and there is still a lack of research on memristors simulating synaptic coupling between neurons in multi-neuron networks.Based on this,this paper uses discrete memristors to couple dual discrete Rulkov neurons,and adds synaptic crosstalk between the two discrete memristors to form a neuronal network.A memristor-coupled dual-neuron map,called the Rulkov-memristor-Rulkov(R-M-R)map,is constructed to simulate synaptic connections between neurons in biological tissues.Then,the equilibrium points of the R-M-R map are studied.Subsequently,the effect of parameter variations on the dynamic performance of the R-M-R map is comprehensively analyzed using bifurcation diagram,phase diagram,Lyapunov exponent spectrum(LEs),firing diagram,and spectral entropy(SE)complexity algorithms.In the RM-R map,diverse categories of periodic,chaotic,and hyperchaotic attractors,as well as different states of firing patterns,can be observed.Additionally,different types of state transitions and coexisting attractors are discovered.Finally,the feasibility of the model in digital circuits is verified using a DSP hardware platform.In this study,the coupling principle of biological neurons is simulated,the chaotic dynamic behavior of the R-M-R map is analyzed,and a foundation is laid for deciphering the complex working mechanisms of the brain.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12172066,61801054,and 51777016)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20160282)the Postgraduate Research and Practice Innovation Program of Jiangsu Province,China(Grant No.KYCX212823)。
文摘Based on the two-dimensional(2D)discrete Rulkov model that is used to describe neuron dynamics,this paper presents a continuous non-autonomous memristive Rulkov model.The effects of electromagnetic induction and external stimulus are simultaneously considered herein.The electromagnetic induction flow is imitated by the generated current from a flux-controlled memristor and the external stimulus is injected using a sinusoidal current.Thus,the presented model possesses a line equilibrium set evolving over the time.The equilibrium set and their stability distributions are numerically simulated and qualitatively analyzed.Afterwards,numerical simulations are executed to explore the dynamical behaviors associated to the electromagnetic induction,external stimulus,and initial conditions.Interestingly,the initial conditions dependent extreme multistability is elaborately disclosed in the continuous non-autonomous memristive Rulkov model.Furthermore,an analog circuit of the proposed model is implemented,upon which the hardware experiment is executed to verify the numerically simulated extreme multistability.The extreme multistability is numerically revealed and experimentally confirmed in this paper,which can widen the future engineering employment of the Rulkov model.
基金supported by the Major Research Plan of the National Natural Science Foundation of China(Grant No.91964108)the National Natural Science Foundation of China(Grant No.61971185)the Natural Science Foundation of Hunan Province,China(Grant No.2020JJ4218).
文摘The exploration of the memristor model in the discrete domain is a fascinating hotspot.The electromagnetic induction on neurons has also begun to be simulated by some discrete memristors.However,most of the current investigations are based on the integer-order discrete memristor,and there are relatively few studies on the form of fractional order.In this paper,a new fractional-order discrete memristor model with prominent nonlinearity is constructed based on the Caputo fractional-order difference operator.Furthermore,the dynamical behaviors of the Rulkov neuron under electromagnetic radiation are simulated by introducing the proposed discrete memristor.The integer-order and fractional-order peculiarities of the system are analyzed through the bifurcation graph,the Lyapunov exponential spectrum,and the iterative graph.The results demonstrate that the fractional-order system has more abundant dynamics than the integer one,such as hyper-chaos,multi-stable and transient chaos.In addition,the complexity of the system in the fractional form is evaluated by the means of the spectral entropy complexity algorithm and consequences show that it is affected by the order of the fractional system.The feature of fractional difference lays the foundation for further research and application of the discrete memristor and the neuron map in the future.
文摘This article proposes a novel fractional heterogeneous neural network by coupling a Rulkov neuron with a Hopfield neural network(FRHNN),utilizing memristors for emulating neural synapses.The study firstly demonstrates the coexistence of multiple firing patterns through phase diagrams,Lyapunov exponents(LEs),and bifurcation diagrams.Secondly,the parameter related firing behaviors are described through two-parameter bifurcation diagrams.Subsequently,local attraction basins reveal multi-stability phenomena related to initial values.Moreover,the proposed model is implemented on a microcomputer-based ARM platform,and the experimental results correspond to the numerical simulations.Finally,the article explores the application of digital watermarking for medical images,illustrating its features of excellent imperceptibility,extensive key space,and robustness against attacks including noise and cropping.
基金the Natural Science Foundation of Hunan Province, China (Grant Nos. 2022JJ30572, 2022JJ30160, and 2021JJ30671)the National Natural Science Foundations of China (Grant No. 62171401)the Key Project of Science and Technology of Shunde District (Grant No. 2130218002544)。
文摘At present, many neuron models have been proposed, which can be divided into discrete neuron models and continuous neuron models. Discrete neuron models have the advantage of faster simulation speed and the ease of understanding complex dynamic phenomena. Due to the properties of memorability, nonvolatility, and local activity, locally active discrete memristors(LADMs) are also suitable for simulating synapses. In this paper, we use an LADM to mimic synapses and establish a Rulkov neural network model. It is found that the change of coupling strength and the initial state of the LADM leads to multiple firing patterns of the neural network. In addition, considering the influence of neural network parameters and the initial state of the LADM, numerical analysis methods such as phase diagram and timing diagram are used to study the phase synchronization. As the system parameters and the initial states of the LADM change, the LADM coupled Rulkov neural network exhibits synchronization transition and synchronization coexistence.
基金Project supported by the Key Projects of Hunan Provincial Department of Education (Grant No.23A0133)the Natural Science Foundation of Hunan Province (Grant No.2022JJ30572)the National Natural Science Foundations of China (Grant No.62171401)。
文摘The brain is a complex network system in which a large number of neurons are widely connected to each other and transmit signals to each other.The memory characteristic of memristors makes them suitable for simulating neuronal synapses with plasticity.In this paper,a memristor is used to simulate a synapse,a discrete small-world neuronal network is constructed based on Rulkov neurons and its dynamical behavior is explored.We explore the influence of system parameters on the dynamical behaviors of the discrete small-world network,and the system shows a variety of firing patterns such as spiking firing and triangular burst firing when the neuronal parameterαis changed.The results of a numerical simulation based on Matlab show that the network topology can affect the synchronous firing behavior of the neuronal network,and the higher the reconnection probability and number of the nearest neurons,the more significant the synchronization state of the neurons.In addition,by increasing the coupling strength of memristor synapses,synchronization performance is promoted.The results of this paper can boost research into complex neuronal networks coupled with memristor synapses and further promote the development of neuroscience.
