Synchronization and multi-frequency oscillations in the low-dimensional chain of the self-oscillators

From chaos to quasi-periodicity

“…To do this, we calculate the spectrum of Lyapunov exponents of the system (2.1) at each point in the parameter plane, and then we color this plane according to the spectrum structure [12][13][14][15]23]. As a result, the following regimes are visualized: P -periodic regime (one zero exponent), T2 -two-frequency quasi-periodic regime (two zero exponents), Cchaos (one positive exponent) and HC -hyperchaos (two positive exponents).…”

“…As a result, multifrequency quasi-periodic oscillations may arise. The invariant tori of higher dimension correspond to these oscillations [9][10][11][12][13][14][15]. With an increase in the coupling, the tori can be destroyed with the formation of chaos.…”

Metamorphoses of resonance curves for two coupled oscillators: The case of small non-linearities in the main mass frame

“…Dynamic vibration absorber is a typical mechanical model described by (1) [1,2] (in this case m is usually much larger than m e ). Dynamics of coupled periodically driven oscillators is very complicated [3][4][5][6][7][8][9][10][11][12][13]. It is important that experimental study confirms good agreement with theoretical model [6].…”

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

“…5(b). The triple Poincaré section on the double Poincaré section is defined as follows: D 2 = (x n , y n , z n , w n , u n , v n ) | |x n − 0.5| < 2 , y n < 0.5, |z n − 0.512| < 3 , w 1 < 0.476 , (7) which is illustrated in Fig. 5(b).…”