Antiperiodic oscillations in Chua’s circuits using conjugate coupling

Chaos-free oscillations

“…The oscillation amplitude decreases with the frequency in the accumulation limit ω → 0, while the period and the number of spikes per period grow. Note the absence of chaos, the T /2 shift between primed and unprimed signals, and that oscillations are antiperiodic [23][24][25][26][27], i.e., they obey eq. ( 2).…”

“…In both figures, the sequence of waveforms reveals an unexpectedly regular and rather symmetrical evolutions. Remarkably, the evolutions are antiperiodic oscillations, a name already used in the 1950s [23][24][25][26][27]. Antiperiodic oscillations are a special type of periodic oscillations which obey the relation…”

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…”