https://doi.org/10.1140/epjp/s13360-022-03510-z
Regular Article
Initial-condition parameterization and dynamical effect of a dual-memelement-based oscillation circuit
School of Microelectronics and Control Engineering, Changzhou University, 213164, Changzhou, China
Received:
21
October
2022
Accepted:
16
November
2022
Published online:
28
November
2022
A novel dual-memelement-based oscillation circuit is established by introducing an ideal flux-controlled memristor and an ideal charge-controlled memcapacitor into the classical Chua’s circuit. The proposed circuit is a five-dimensional system and possesses a plane equilibrium set. The eigenpolynomial of Jacobian matrix at each equilibrium point has two zero eigenvalues since the involvement of the two ideal memelements. The emergence of the two zero eigenvalues makes that it is infeasible to precisely analyze the stability of the five-dimensional system. To precisely analyze the system stability, the incremental integral transformation method is utilized to convert the five-dimensional system equations into three-dimensional system equations. In the new reconstituted system, the plane equilibrium set is mapped to finite equilibrium points which display determined stability. Moreover, the initial conditions in the original system are explicitly expressed in the reconstituted system equations in the form of initial-condition-related parameters, aka initial-condition parameterization. Dynamical effects of initial-condition-related parameters of the memelement and non-memelement are revealed by bifurcation analyses and phase trajectories. What is more, the FPGA-based hardware implementation and experimental measure are executed to verify the correctness of the numerical analysis.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
