A memcapacitor is a new type of memory capacitor. Before the advent of practical memcapacitor, the prospective studies on its models and potential applications are of importance. For this purpose, we establish a mathe...A memcapacitor is a new type of memory capacitor. Before the advent of practical memcapacitor, the prospective studies on its models and potential applications are of importance. For this purpose, we establish a mathematical memca- pacitor model and a corresponding circuit model. As a potential application, based on the model, a memcapacitor oscillator is designed, with its basic dynamic characteristics analyzed theoretically and experimentally. Some circuit variables such as charge, flux, and integral of charge, which are difficult to measure, are observed and measured via simulations and exper- iments. Analysis results show that besides the typical period-doubling bifurcations and period-3 windows, sustained chaos with constant Lyapunov exponents occurs. Moreover, this oscillator also exhibits abrupt chaos and some novel bifurcations. In addition, based on the digital signal processing （DSP） technology, a scheme of digitally realizing this memcapacitor os- cillator is provided. Then the statistical properties of the chaotic sequences generated from the oscillator are tested by using the test suit of the National Institute of Standards and Technology （NIST）. The tested randomness definitely reaches the standards of NIST, and is better than that of the well-known Lorenz system.展开更多
In this paper, by referring to the concept of coupled memristors （MRs） and considering the flux coupling connection, the constitutive relations for describing the coupled memcapacitors （MCs） are theoretically dedu...In this paper, by referring to the concept of coupled memristors （MRs） and considering the flux coupling connection, the constitutive relations for describing the coupled memcapacitors （MCs） are theoretically deduced. The dynamic behaviors of dual coupled MCs in serial and parallel connections are analyzed in terms of identical or opposite polarities for the first time. Based on the derived constitutive relations of the two coupled MCs, the modified relaxation oscillators （ROs） are obtained with the purpose of achieving controllable oscillation frequency and duty cycle. In consideration of different parameter configurations, the experimental investigation is carried out by using practical off-the-shelf circuit components to verify the correction of the theoretical calculation with numerical simulation of the coupled MCs and its application in ROs.展开更多
Recently,the memory elements-based circuits have been addressed frequently in the nonlinear circuit theory due to their unique behaviors.Thus,the modeling and characterizing of the mem-elements become essential.In thi...Recently,the memory elements-based circuits have been addressed frequently in the nonlinear circuit theory due to their unique behaviors.Thus,the modeling and characterizing of the mem-elements become essential.In this paper,the analysis of the multiple fractional-order voltage-controlled memcapacitors model in parallel connection is studied.Firstly,two fractional-order memcapacitors are connected in parallel,the equivalent model is derived,and the characteristic of the equivalent memcapacitor is analyzed in positive or negative connection.Then a new understanding manner according to different rate factor K and fractional orderαis derived to explain the equivalent modeling structure conveniently.Additionally,the negative order appears,which is a consequence of the combination of memcapacitors in different directions.Meanwhile,the equivalent parallel memcapacitance has been drawn to determine that multiple fractional-order memcapacitors could be calculated as one composite memcapacitor.Thus,an arbitrary fractional-order equivalent memcapacitor could be constructed by multiple fractional-order memcapacitors.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 Nos.61271064,61401134and 60971046)+1 种基金the Natural Science Foundation of Zhejiang Province,China(Grant Nos.LZ12F01001 and LQ14F010008)the Program for Zhejiang Leading Team of S&T Innovation,China(Grant No.2010R50010)
文摘A memcapacitor is a new type of memory capacitor. Before the advent of practical memcapacitor, the prospective studies on its models and potential applications are of importance. For this purpose, we establish a mathematical memca- pacitor model and a corresponding circuit model. As a potential application, based on the model, a memcapacitor oscillator is designed, with its basic dynamic characteristics analyzed theoretically and experimentally. Some circuit variables such as charge, flux, and integral of charge, which are difficult to measure, are observed and measured via simulations and exper- iments. Analysis results show that besides the typical period-doubling bifurcations and period-3 windows, sustained chaos with constant Lyapunov exponents occurs. Moreover, this oscillator also exhibits abrupt chaos and some novel bifurcations. In addition, based on the digital signal processing （DSP） technology, a scheme of digitally realizing this memcapacitor os- cillator is provided. Then the statistical properties of the chaotic sequences generated from the oscillator are tested by using the test suit of the National Institute of Standards and Technology （NIST）. The tested randomness definitely reaches the standards of NIST, and is better than that of the well-known Lorenz system.
基金Project supported by the Fundamental Research Funds for China Central Universities(Grant No.2015XKMS028)
文摘In this paper, by referring to the concept of coupled memristors （MRs） and considering the flux coupling connection, the constitutive relations for describing the coupled memcapacitors （MCs） are theoretically deduced. The dynamic behaviors of dual coupled MCs in serial and parallel connections are analyzed in terms of identical or opposite polarities for the first time. Based on the derived constitutive relations of the two coupled MCs, the modified relaxation oscillators （ROs） are obtained with the purpose of achieving controllable oscillation frequency and duty cycle. In consideration of different parameter configurations, the experimental investigation is carried out by using practical off-the-shelf circuit components to verify the correction of the theoretical calculation with numerical simulation of the coupled MCs and its application in ROs.
基金the National Natural Science Foundation of China(Grant No.52077160).
文摘Recently,the memory elements-based circuits have been addressed frequently in the nonlinear circuit theory due to their unique behaviors.Thus,the modeling and characterizing of the mem-elements become essential.In this paper,the analysis of the multiple fractional-order voltage-controlled memcapacitors model in parallel connection is studied.Firstly,two fractional-order memcapacitors are connected in parallel,the equivalent model is derived,and the characteristic of the equivalent memcapacitor is analyzed in positive or negative connection.Then a new understanding manner according to different rate factor K and fractional orderαis derived to explain the equivalent modeling structure conveniently.Additionally,the negative order appears,which is a consequence of the combination of memcapacitors in different directions.Meanwhile,the equivalent parallel memcapacitance has been drawn to determine that multiple fractional-order memcapacitors could be calculated as one composite memcapacitor.Thus,an arbitrary fractional-order equivalent memcapacitor could be constructed by multiple fractional-order memcapacitors.
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.
