Analysis of a Belyakov homoclinic connection with ℤ2-symmetry

Chua Circuit based on the Exponential Characteristics of Semiconductor Devices

“…Other nonlinearities have been proposed for Chua diode, such as cubic polynomial functions and "cubic-like" approximations (Zhong, 1994;Eltawil and Elwakil, 1999;O'Donoghue et al, 2005;Tsuneda, 2005;Rocha and Medrano-T., 2020), sigmoid and signum functions (Brown, 1993), odd square law ax + bx|x| (Tang and Man, 1998), trigonometric functions (Tang et al, 2001), memristive current-voltage characteristics (Rocha et al, 2017), etc. In despite of its simplicity, the Chua circuit generates a great diversity of nonlinear phenomena such as fixed and equilibrium points, periodic and stranger attractors, Andronov-Hopf, saddle-node (tangent), flip (period-doubling), cusp, homoclinic, heteroclinic, and other kinds of bifurcations, multistability and hidden oscillations, antiperiodic oscillations, period-adding in sets of periodicity, metamorphoses of basins of attraction, etc (Madan, 1993;Medrano-T. et al, 2005;Algaba et al, 2012;Leonov and Kuznetsov, 2013;Medrano-T. and Rocha, 2014;Singla et al, 2015;Menacer et al, 2016;Bao et al, 2016Bao et al, , 2018Singla et al, 2018;Liu et al, 2020;Wang et al, 2021). The most of these nonlinear phenomena occur in the parameter range α < β < γ 2 (Rocha and Medrano-T., 2020Medrano-T., , 2015Medrano-T., , 2016Rocha et al, 2017), where…”

The Negative Side of Chua's Circuit Parameter Space: Stability Analysis, Period-Adding, Basin of Attraction Metamorphoses, and Experimental Investigation

“…Chua's circuit is a paradigm in nonlinear dynamics and has been extensively studied since 1984 [Matsumoto, 1984]. This simple electric circuit presents a dynamics with a wide diversity of attractors [Matsumoto, 1984;Matsumoto et al, 1987], a strictly proven chaotic behavior in the sense of Shilnikov theorem [Chua et al, 1986], and fundamental phenomena such as Andronov-Hopf, saddle-node (tangent), flip (period-doubling), cusp, homoclinic, heteroclinic, and many other kinds of bifurcations [Matsumoto et al, 1986;Bykov, 1998;Medrano-T et al, 2003Medrano-T et al, , 2005Medrano-T et al, , 2006Algaba et al, 2012]. In this system, domains of periodicity immersed in chaotic regions of 2D parameter space are organized in period-adding cascades with spiral configurations along homoclinic bifurcations [Komuro et al, 1991;Albuquerque & Rech, 2012].…”