Most of nonlinear oscillators composed of capacitive and inductive variables can obtain the Hamilton energy by using the Helmholtz theorem when the models are rewritten in equivalent vector forms.The energy functions ...Most of nonlinear oscillators composed of capacitive and inductive variables can obtain the Hamilton energy by using the Helmholtz theorem when the models are rewritten in equivalent vector forms.The energy functions for biophysical neurons can be obtained by applying scale transformation on the physical field energy in their equivalent neural circuits.Realistic dynamical systems often have exact energy functions,while some mathematical models just suggest generic Lyapunov functions,and the energy function is effective to predict mode transition.In this paper,a memristive oscillator is approached by two kinds of memristor-based nonlinear circuits,and the energy functions are defined to predict the dependence of oscillatory modes on energy level.In absence of capacitive variable for capacitor,the physical time t and charge q are converted into dimensionless variables by using combination of resistance and inductance(L,R),e.g.,τ=t×R/L.Discrete energy function for each memristive map is proposed by applying the similar weights as energy function for the memristive oscillator.For example,energy function for the map is obtained by replacing the variables and parameters of the memristive oscillator with corresponding variables and parameters for the memristive map.The memristive map prefers to keep lower average energy than the memristive oscillator,and chaos is generated in a discrete system with two variables.The scheme is helpful for energy definition in maps,and it provides possible guidance for verifying the reliability of maps by considering the energy characteristic.展开更多
A functional neuron has been developed from a simple neural circuit by incorporating a phototube and a thermistor in different branch circuits.The physical field energy is controlled by the photocurrent across the pho...A functional neuron has been developed from a simple neural circuit by incorporating a phototube and a thermistor in different branch circuits.The physical field energy is controlled by the photocurrent across the phototube and the channel current across the thermistor.The firing mode of this neuron is controlled synchronously by external temperature and illumination.There is energy diversity when two functional neurons are exposed to different illumination and temperature conditions.As a result,synapse connections can be created and activated in an adaptive way when field energy is exchanged between neurons.We propose two kinds of criteria to discuss the enhancement of synapse connections to neurons.The energy diversity between neurons determines the increase of the coupling intensity and synaptic current for neurons,and the realization of synchronization is helpful in maintaining energy balance between neurons.The first criterion is similar to the saturation gain scheme in that the coupling intensity is increased with a constant step within a certain period until it reaches energy balance or complete synchronization.The second criterion is that the coupling intensity increases exponentially before reaching energy balance.When two neurons become non-identical,phase synchronization can be controlled during the activation of synapse connections to neurons.For two identical neurons,the second criterion for taming synaptic intensity is effective for reaching complete synchronization and energy balance,even in the presence of noise.This indicates that a synapse connection may prefer to enhance its coupling intensity exponentially.These results are helpful in discovering why synapses are awaken and synaptic current becomes time-varying when any neurons are excited by external stimuli.The potential biophysical mechanism is that energy balance is broken and then synapse connections are activated to maintain an adaptive energy balance between the neurons.These results provide guidance for designing and training intellige展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12072139)。
文摘Most of nonlinear oscillators composed of capacitive and inductive variables can obtain the Hamilton energy by using the Helmholtz theorem when the models are rewritten in equivalent vector forms.The energy functions for biophysical neurons can be obtained by applying scale transformation on the physical field energy in their equivalent neural circuits.Realistic dynamical systems often have exact energy functions,while some mathematical models just suggest generic Lyapunov functions,and the energy function is effective to predict mode transition.In this paper,a memristive oscillator is approached by two kinds of memristor-based nonlinear circuits,and the energy functions are defined to predict the dependence of oscillatory modes on energy level.In absence of capacitive variable for capacitor,the physical time t and charge q are converted into dimensionless variables by using combination of resistance and inductance(L,R),e.g.,τ=t×R/L.Discrete energy function for each memristive map is proposed by applying the similar weights as energy function for the memristive oscillator.For example,energy function for the map is obtained by replacing the variables and parameters of the memristive oscillator with corresponding variables and parameters for the memristive map.The memristive map prefers to keep lower average energy than the memristive oscillator,and chaos is generated in a discrete system with two variables.The scheme is helpful for energy definition in maps,and it provides possible guidance for verifying the reliability of maps by considering the energy characteristic.
基金Project supported by the National Natural Science Foundation of China(No.12072139)。
文摘A functional neuron has been developed from a simple neural circuit by incorporating a phototube and a thermistor in different branch circuits.The physical field energy is controlled by the photocurrent across the phototube and the channel current across the thermistor.The firing mode of this neuron is controlled synchronously by external temperature and illumination.There is energy diversity when two functional neurons are exposed to different illumination and temperature conditions.As a result,synapse connections can be created and activated in an adaptive way when field energy is exchanged between neurons.We propose two kinds of criteria to discuss the enhancement of synapse connections to neurons.The energy diversity between neurons determines the increase of the coupling intensity and synaptic current for neurons,and the realization of synchronization is helpful in maintaining energy balance between neurons.The first criterion is similar to the saturation gain scheme in that the coupling intensity is increased with a constant step within a certain period until it reaches energy balance or complete synchronization.The second criterion is that the coupling intensity increases exponentially before reaching energy balance.When two neurons become non-identical,phase synchronization can be controlled during the activation of synapse connections to neurons.For two identical neurons,the second criterion for taming synaptic intensity is effective for reaching complete synchronization and energy balance,even in the presence of noise.This indicates that a synapse connection may prefer to enhance its coupling intensity exponentially.These results are helpful in discovering why synapses are awaken and synaptic current becomes time-varying when any neurons are excited by external stimuli.The potential biophysical mechanism is that energy balance is broken and then synapse connections are activated to maintain an adaptive energy balance between the neurons.These results provide guidance for designing and training intellige
