Circuit simulation demonstrates integrability conditions in nonlinear dynamical systems, suggesting new validation methods.
Abstract Up to now, most research papers of integrability of differential equations are emphasized on theoretical proof. However, there is no work about experimental verification of integrability. To solve the problem, this paper we focus on circuit simulation experiment of the integrability of nonlinear dynamical systems. The integrability of nonlinear dynamical systems is investigated by circuit simulation experiment. The integrability conditions for three kinds of nonlinear systems are reviewed. Then, the circuit diagrams corresponding to the nonlinear systems are designed by using Kirchhoff’s law, the circuit models are established via the Multisim 14.0 simulation software. The realization of the integrable nonlinear systems in the circuit is examined, and the results of the analytical solutions of the equations are compared with the simulation results of the circuit, the circuit simulation experiment indicates that the simulation results support the analytical solutions. It is further proved that the integrability of nonlinear systems is effective.
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Song et al. (2025) studied this question.
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