Biolek Zdeněk, Biolek Dalibor, Biolková Viera, Kolka Zdeněk
Department of Microelectronics, Brno University of Technology, 616 00 Brno, Czech Republic.
Department of Electrical Engineering, University of Defence, 662 10 Brno, Czech Republic.
Entropy (Basel). 2020 Apr 5;22(4):412. doi: 10.3390/e22040412.
The paper studies the construction of the Hamiltonian for circuits built from the (,) elements of Chua's periodic table. It starts from the Lagrange function, whose existence is limited to Σ-circuits, i.e., circuits built exclusively from elements located on a common Σ-diagonal of the table. We show that the Hamiltonian can also be constructed via the generalized Tellegen's theorem. According to the ideas of predictive modeling, the resulting Hamiltonian is made up exclusively of the constitutive relations of the elements in the circuit. Within the frame of Ostrogradsky's formalism, the simulation scheme of Σ-circuits is designed and examined with the example of a nonlinear Pais-Uhlenbeck oscillator.
本文研究了由蔡氏周期表中的（，）元件构成的电路哈密顿量的构建。它从拉格朗日函数出发，其存在仅限于Σ电路，即仅由位于该表公共Σ对角线上的元件构成的电路。我们表明，哈密顿量也可以通过广义特勒根定理来构建。根据预测建模的思想，所得哈密顿量仅由电路中元件的本构关系组成。在奥斯特罗格拉德斯基形式体系的框架内，以非线性派斯 - 乌伦贝克振荡器为例，设计并检验了Σ电路的仿真方案。
