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
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.
