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
This study constructs a dual-capacitor neuron circuit(connected via a memristor)integrated with a phototube and a thermistor to simulate the ability of biological neurons to simultaneously perceive light and thermal s...This study constructs a dual-capacitor neuron circuit(connected via a memristor)integrated with a phototube and a thermistor to simulate the ability of biological neurons to simultaneously perceive light and thermal stimuli.The circuit model converts photothermal signals into electrical signals,and its dynamic behavior is described using dimensionless equations derived from Kirchhoff's laws.Based on Helmholtz's theorem,a pseudo-Hamiltonian energy function is introduced to characterize the system's energy metabolism.Furthermore,an adaptive control function is proposed to elucidate temperature-dependent firing mechanisms,in which temperature dynamics are regulated by pseudo-Hamiltonian energy.Numerical simulations using the fourth-order Runge-Kutta method,combined with bifurcation diagrams,Lyapunov exponent spectra,and phase portraits,reveal that parameters such as capacitance ratio,phototube voltage amplitude/frequency,temperature,and thermistor reference resistance significantly modulate neuronal firing patterns,inducing transitions between periodic and chaotic states.Periodic states typically exhibit higher average pseudo-Hamiltonian energy than chaotic states.Two-parameter analysis demonstrates that phototube voltage amplitude and temperature jointly govern firing modes,with chaotic behavior emerging within specific parameter ranges.Adaptive control studies show that gain/attenuation factors,energy thresholds,ceiling temperatures,and initial temperatures regulate the timing and magnitude of system temperature saturation.During both heating and cooling phases,temperature dynamics are tightly coupled with pseudoHamiltonian energy and neuronal firing activity.These findings validate the circuit's ability to simulate photothermal perception and adaptive temperature regulation,contributing to a deeper understanding of neuronal encoding mechanisms and multimodal sensory processing.展开更多
The output voltages for the capacitive elements of a neural circuit model can be mapped into dimensionless capacitive variables,which present firing patterns similar to the membrane potentials detected in biological n...The output voltages for the capacitive elements of a neural circuit model can be mapped into dimensionless capacitive variables,which present firing patterns similar to the membrane potentials detected in biological neurons.The inclusion of a memcapacitor also en‐ables consideration of membrane deformation effects,enhancing the model’s capacity to simulate neuronal behavior across varying physio‐logical and environmental conditions.In this study,a capacitor and a memcapacitor are connected through a linear resistor in parallel with other electric components in different branch circuits composed of an inductor and a nonlinear resistor.The electrical activities in a neuron with a double-layer membrane and two capacitive variables are discussed in detail after converting the nonlinear equations for the neural circuit into a theoretical neuron model.A dimensionless neuron model and its corresponding energy function are derived.The field energy function for the neural circuit is converted into an equivalent Hamilton energy function and further validated via the Helmholtz theorem.Furthermore,the average value of energy serves as an indicator for predicting stochastic resonance,as supported by analyzing the distribu‐tion of the coefficient of variation.The neuronal firing patterns are shown to be energy-dependent.An adaptive control strategy is proposed to regulate mode transitions in electrical activities of the neuron.An analog equivalent circuit is constructed to experimentally verify the nu‐merical results,thereby supporting the reliability of the proposed neuron model.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supported by the Natural Science Founda tion of Chongqing(Grant No.CSTB2024NSCQ-MSX0944)。
文摘This study constructs a dual-capacitor neuron circuit(connected via a memristor)integrated with a phototube and a thermistor to simulate the ability of biological neurons to simultaneously perceive light and thermal stimuli.The circuit model converts photothermal signals into electrical signals,and its dynamic behavior is described using dimensionless equations derived from Kirchhoff's laws.Based on Helmholtz's theorem,a pseudo-Hamiltonian energy function is introduced to characterize the system's energy metabolism.Furthermore,an adaptive control function is proposed to elucidate temperature-dependent firing mechanisms,in which temperature dynamics are regulated by pseudo-Hamiltonian energy.Numerical simulations using the fourth-order Runge-Kutta method,combined with bifurcation diagrams,Lyapunov exponent spectra,and phase portraits,reveal that parameters such as capacitance ratio,phototube voltage amplitude/frequency,temperature,and thermistor reference resistance significantly modulate neuronal firing patterns,inducing transitions between periodic and chaotic states.Periodic states typically exhibit higher average pseudo-Hamiltonian energy than chaotic states.Two-parameter analysis demonstrates that phototube voltage amplitude and temperature jointly govern firing modes,with chaotic behavior emerging within specific parameter ranges.Adaptive control studies show that gain/attenuation factors,energy thresholds,ceiling temperatures,and initial temperatures regulate the timing and magnitude of system temperature saturation.During both heating and cooling phases,temperature dynamics are tightly coupled with pseudoHamiltonian energy and neuronal firing activity.These findings validate the circuit's ability to simulate photothermal perception and adaptive temperature regulation,contributing to a deeper understanding of neuronal encoding mechanisms and multimodal sensory processing.
基金supported by the National Natural Science Foundation of China(No.12072139).
文摘The output voltages for the capacitive elements of a neural circuit model can be mapped into dimensionless capacitive variables,which present firing patterns similar to the membrane potentials detected in biological neurons.The inclusion of a memcapacitor also en‐ables consideration of membrane deformation effects,enhancing the model’s capacity to simulate neuronal behavior across varying physio‐logical and environmental conditions.In this study,a capacitor and a memcapacitor are connected through a linear resistor in parallel with other electric components in different branch circuits composed of an inductor and a nonlinear resistor.The electrical activities in a neuron with a double-layer membrane and two capacitive variables are discussed in detail after converting the nonlinear equations for the neural circuit into a theoretical neuron model.A dimensionless neuron model and its corresponding energy function are derived.The field energy function for the neural circuit is converted into an equivalent Hamilton energy function and further validated via the Helmholtz theorem.Furthermore,the average value of energy serves as an indicator for predicting stochastic resonance,as supported by analyzing the distribu‐tion of the coefficient of variation.The neuronal firing patterns are shown to be energy-dependent.An adaptive control strategy is proposed to regulate mode transitions in electrical activities of the neuron.An analog equivalent circuit is constructed to experimentally verify the nu‐merical results,thereby supporting the reliability of the proposed neuron model.
