Bifurcation analysis of four-frequency quasi-periodic oscillations in a three-coupled delayed logistic map

Chaos in a second-order non-autonomous Wien-bridge oscillator without extra nonlinearity

“…Quasi-periodic oscillation often arises from multi-frequency (Guskov et al, 2008;Pusenjak and Oblak, 2003), singlefrequency (Hidaka et al, 2015) and nonlocal Boussinesq equation (Bashkirtseva et al, 2015), in which the quasiperiodic response can be represented by a multi-dimensional Fourier series with the ratio of any two basic frequencies irrationally (Ji and Bi, 2010;Zhou et al, 2015). Although the quasi-periodic solutions and the stabilities of the previously proposed systems have been obtained analytically and numerically, the circuit implementations by operational amplifiers and analog multipliers are complex unluckily and few research reports are related to the important phenomenon of quasi-periodic oscillation in the realistic electronic circuit.…”

Numerical and experimental observation of Arnol’d resonance webs in an electrical circuit

“…They showed that a stable three-dimensional torus occurs because of the saddle-node bifurcation of a stable two-dimensional torus and a saddle twodimensional torus. Anishchenkos' and our previous results [14,15] strongly suggest that a stable (n + 1)-dimensional torus emerges because of the saddle-node bifurcation of the stable and saddle n-dimensional tori, which is identified as a QSN bifurcation. Such bifurcation structures are noteworthy.…”

Stability of the 3-torus solution in a ring of coupled Duffing oscillators

“…N ≥ 3) has been reported also a e-mail: andrzej.stefanski@p.lodz.pl in sets of coupled systems [12,[15][16][17][18][19][23][24][25][26][27][28][29] and self or externally driven oscillators [30][31][32][33]. Other notable cases of such solutions (four-and five-frequency torus) have been recently demonstrated in systems of chains or globally coupled phase oscillators with frequency detuning [34,35] and in system of linked delayed logistic maps [36].…”