Affiliation:
1. Departamento de Física, Universidade do Estado de Santa Catarina (UDESC), 89219-710 Joinville, SC, Brazil
2. Instituto de Matemática e Computação, Universidade Federal de Itajubá (UNIFEI), 37500-903 Itajubá, MG, Brazil
Abstract
The three-dimensional Muthuswamy–Chua–Ginoux (MCG) circuit model is a generalization of the paradigmatic canonical Muthuswamy–Chua circuit, where a physical memristor assumes the role of a thermistor, and it is connected in series with a linear passive capacitor, a linear passive inductor, and a nonlinear resistor. The physical memristor presents an electrical resistance which is a function of temperature. Nowadays, the MCG circuit model has gained considerable attention due to the lack of extensive numerical explorations and their distinct dynamical properties, exemplified by phenomena such as the transition from torus breakdown to chaos, giving rise to a double spiral attractor associated to independent period-doubling cascades. In this contribution, the complex dynamics of the MCG circuit model is studied in terms of the Lyapunov exponents spectra, Kaplan–Yorke (KY) dimension, and the number of local maxima (LM) computed in one period of oscillation, as two parameters are simultaneously varied. Using the Lyapunov spectra to distinguish different dynamical regimes, KY dimension to estimate the attractors’ dimension, and the number of LM to characterize different periodic attractors, we construct high-resolution two-dimensional stability diagrams considering specific ranges of the parameter pairs [Formula: see text]. These parameters are associated with the inverse of the capacitance in the passive capacitor, and the heat capacitance and dissipation constant of the thermistor, respectively. Unexpectedly, we identify sequences of infinite self-organized generic stable periodic structures (SPSs) and Arnold tongues-like structures (ATSs) merged into chaotic dynamics domains, and the coexistence of different attracting sets (attractors) for the same parameter combinations and different initial conditions (multistability). We explore the multistable dynamics using the stability analysis and computation of Lyapunov coefficients, the inspection of the coexisting attractors, bifurcations diagrams, and basins of attraction. The periods of the ATSs and a particular sequence of shrimp-shaped SPSs obey specific generating and recurrence rules responsible for the bifurcation cascades. As the MCG circuit model has the crucial properties presented by the usual Muthuswamy–Chua circuit model, specific properties explored in our study should be helpful in real problems involving circuits with the presence of physical memristor playing the role of thermistors.
Funder
National Council for Scientific and Technological Development
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Fundação de Amparo à Pesquisa e Inovação do Estado de Santa Catarina
Fundação de Amparo á Pesquisa do Estado de Sáo Paulo
Fundação de Amparo á Pesquisa do Estado de Minas Gerais
Fundação de Amparo á Pesquisa e Inovação do Estado de Santa Catarina
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)