Reverse Newhouse–Ruelle–Takens route to chaos and time-dependent Hamiltonian formulation of a generalized Muthuswamy–Chua system

This work introduces a generalization of the Muthuswamy-Chua system of equations. The generalization allows us to embed memristive/hysteretic systems in a time-varying Hamiltonian, which acts as an energy-like Lyapunov function, whose growth or decay is governed by the memristor feedback and by whether the oscillator is momentarily kinetic- or potential-dominated. We perform mathematical analysis and detailed numerical investigations of the fourth-order Muthuswamy-Chua system based on bifurcation diagram and Lyapunov characteristic exponents. We then highlight bifurcation routes from torus breakdown to homoclinic chaos following the Newhouse-Ruelle-Takens scenario. The corresponding electronic oscillator is then analyzed and validated by SPICE (Simulation Program with Integrated Circuit Emphasis) simulations. To our knowledge, our work represents a novel memristive approach to describing a harmonic oscillator interacting with a finite "bath."