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The contribution is concerned on the introduction of mem-devices as a replacement for the nonlinear part of the hyperbolicity problem in circuit theory. These memory devices whose properties cannot be reproduced with standard resistors, capacitors and inductors were considered as “fundamental” circuit elements. In this paper, we focused on the purely imaginary eigenvalues (PIE) obtained from extended Duffing(Do), Duffing Van Der Pol (DVPo) and Bonhoeffer Van Der Pol (BVPo) oscillators. This work is based on semistate or differential-algebraic circuits equations, matrix notions and diagraph theory. We discovered that PIE only exist in extended Duffing Van Der Pol oscillators and extended Bonhoeffer van Der Pol oscillators due to the presence of LC block.

Purely Imaginary Eigenvalues (PIE) in Extended Circuits with Mem-Devices