The flow of electric current through the chain of nonlinear inertial resistors and capacitors

The stability conditions for an electric current flowing through a chain consisting of nonlinear inertial resistors and capacitors have been investigated. The necessary conditions for the field dependent conductivity and the inertia of the resistors and applied voltage leading to undamped oscillations in the chain have been derived. For the threshold voltage this condition has the form ₀+V ₀(/V) _v0 cos _I ^T =0, similar to that obtained in an earlier work of one of the authors from thermodynamical considerations.Computer simulation gives results for the frequency and threshold conditions in good agreement with approximate analytical solutions.