Reverse Newhouse-Ruelle-Takens route to chaos and time-dependent Hamiltonian formulation of a generalized Muthuswamy-Chua system
Year: 2026
Authors: Muthuswamy B., Ginoux J.M., Concas R., Meucci R., Llibre J., Chua L.O.
Autors Affiliation: NERD Inc, Nonlinear Engn Res & Dev, San Jose, CA 95121 USA; Aix Marseille Univ, Univ Toulon, CNRS, LIS, Toulon, France; Ist Nazl Ric Metrolog, Sesto Fiorentino, Florence, Italy; CNR, Natl Inst Opt, Florence, Italy; Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Barcelona, Spain; Univ Calif Berkeley, Dept EECS, Berkeley, CA 94720 USA.
Abstract: 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.
Journal/Review: CHAOS
Volume: 36 (1) Pages from: 13132-1 to: 13132-13
More Information: The authors would like to thank the reviewers for their helpful advice, which enabled them to improve the quality of this work. J. Llibre is partially supported by the Agencia Estatal de Investigacion of Spain grant PID2022-136613NB-100.KeyWords: article; human; integrated circuit; kinetics; mathematical analysis; memristor; oscillator; simulation; spiceDOI: 10.1063/5.0304010
