利用运算放大器和乘法器进行电路设计,对早期利用电子管实现的Van der Pol振荡器利用现代集成电路加以实现。文中还利用OrCAD PSpice对设计的电路进行了模拟,得到了Van der Pol振荡器输出信号的波形图,并利用文本文件作为OrCAD PSpice和...利用运算放大器和乘法器进行电路设计,对早期利用电子管实现的Van der Pol振荡器利用现代集成电路加以实现。文中还利用OrCAD PSpice对设计的电路进行了模拟,得到了Van der Pol振荡器输出信号的波形图,并利用文本文件作为OrCAD PSpice和Matlab之间的接口,将OrCAD PSpice仿真得到的波形在Matlab中进行处理,得到Van der Pol振荡器两个状态变量的相图,并以此说明了Van der Pol振荡器所具有的丰富的非线性动力学特性。展开更多
This paper presents an alternative representation of a system of differential equations qualitatively showing the behavior of the biological rhythm of a crayfish during their transition from juvenile to adult stages. ...This paper presents an alternative representation of a system of differential equations qualitatively showing the behavior of the biological rhythm of a crayfish during their transition from juvenile to adult stages. The model focuses on the interaction of four cellular oscillators coupled by diffusion of a hormone, a parameter μ is used to simu- late the quality of communication among the oscillators, in biological terms, it mea- sures developmental maturity of the crayfish. Since some quorum-sensing mechanism is assumed to be responsible for the synchronization of the biological oscillators, it is nat- ural to investigate the possibility that the underlying diffusion process is not standard, i.e. it may be a so-called anomalous diffusion. In this case, it is well understood that diffusion equations with fractional derivatives describe these processes in a more realis- tic way. The alternative formulation of these equations contains fractional operators of Liouville-Caputo and Caputo-Fabrizio type. The numerical simulations of the equations reflect synchronization of ultradian rhythms leading to a circadian rhythm. The classical behavior is recovered when the order of the fractional derivative is V = 1. We discuss possible biological implications.展开更多
文摘利用运算放大器和乘法器进行电路设计,对早期利用电子管实现的Van der Pol振荡器利用现代集成电路加以实现。文中还利用OrCAD PSpice对设计的电路进行了模拟,得到了Van der Pol振荡器输出信号的波形图,并利用文本文件作为OrCAD PSpice和Matlab之间的接口,将OrCAD PSpice仿真得到的波形在Matlab中进行处理,得到Van der Pol振荡器两个状态变量的相图,并以此说明了Van der Pol振荡器所具有的丰富的非线性动力学特性。
文摘This paper presents an alternative representation of a system of differential equations qualitatively showing the behavior of the biological rhythm of a crayfish during their transition from juvenile to adult stages. The model focuses on the interaction of four cellular oscillators coupled by diffusion of a hormone, a parameter μ is used to simu- late the quality of communication among the oscillators, in biological terms, it mea- sures developmental maturity of the crayfish. Since some quorum-sensing mechanism is assumed to be responsible for the synchronization of the biological oscillators, it is nat- ural to investigate the possibility that the underlying diffusion process is not standard, i.e. it may be a so-called anomalous diffusion. In this case, it is well understood that diffusion equations with fractional derivatives describe these processes in a more realis- tic way. The alternative formulation of these equations contains fractional operators of Liouville-Caputo and Caputo-Fabrizio type. The numerical simulations of the equations reflect synchronization of ultradian rhythms leading to a circadian rhythm. The classical behavior is recovered when the order of the fractional derivative is V = 1. We discuss possible biological implications.
