Stability analysis of a class of electronic circuits based on thermodynamic principles part I: analysis of limit cycles

In this first of a two-part manuscript, internal entropy production is used as a Lyapunov function for complex systems consisting of a class of electronic circuits. Since the ultimate aim of this paper is to study and discuss the stability and the dynamical behavior of a nonlinear electronic oscillator, stability properties are progressively analyzed by disassembling this complex system into two simpler study cases and by the identification of recurring subsystems. The internal entropy production approach allows conservative and dissipative phenomena of the system and their interactions to be identified when applied to thermodynamically consistent models. Additionally, by splitting up a more complex system, this approach lets us understand the separate effect of each element in the whole system. Numerical simulations are carried out for specific conditions to support analytical results. Complex dynamical behaviors, including limit cycles, are addressed with entropic and energetic perspectives. It is observed that the presence of different characteristic times among subsystems, like those induced by nearly infinite reservoirs inside the system, impacts thermodynamic balances of conserved quantities and maintains the system out of thermodynamic equilibrium. Internal entropy production permits to either address stability of fixed points forthwith as a Lyapunov function or define regions of attraction to trajectories. Multiplicity of steady states and appearance of limit cycles, which are related to destabilizing interactions when far from equilibrium, might shed light on thermodynamics of deterministic chaos and emergence of complexity.