Quadrature Synchronization of Two Van der Pol Oscillators Coupled by Fractional-Order Derivatives

Synchronization and amplitude death in a pair of Van der Pol oscillators under conjugate coupling

“…In the case of weak coupling corresponding to k 0.03 = (that is, prior to the onset of amplitude death region, see figure 1) the phase synchronization occurs if there is no detuning, figures 5(a) and (b). This is in tune with equation (17). However, in the amplitude death region (k 0.2, = see figure 1) with finite detuning the final state of synchronization is not affected whether the initial conditions are identical or not.…”

“…The quadrature phase signals are important for signal processing in modern electrical communication systems. In [16,17] two capacitive coupling of VdP oscillators were analyzed to produce quadrature harmonic signals. The extensive and rigorous theoretical analyses of coupled self-sustained oscillators under diffusive coupling have been studied for the perspective of synchronization and amplitude death and their potential applications are discussed [2,18,19,35,36].…”

“…The coupling of two or more VdP oscillators produces rich dynamical behavior depending upon the value of nonlinearity parameter (e), type of coupling and coupling strength. The dynamics of coupled VdP oscillators is of interest to prototype modeling of many biological and engineering phenomena such as the dynamics of heartbeat [2][3][4], the circadian rhythms in eyes of vertebrates [5,6], the excitatory and inhibitory neuronal activities [7], the phaselocked control and structural stability [8][9][10][11][12][13], the network synchronization [14,15] and the generation of multiphase communication signals [16,17]. Earlier studies on coupled VdP oscillators dynamics involved diffusive coupling via displacement and/or velocity fields [3][4][5][6][7][8][9][10] and delayed couplings [11][12][13][14].…”