Dynamics of three unidirectionally coupled modified van der Pol oscillators

Abstract

The dynamics of three unidirectionally coupled modified van der Pol oscillators with time fractional derivatives is studied via phase-space and time evolution plots using Fractional Predict-Evaluate-Correct-Evaluate (FracPECE) numerical integrator. The three oscillators differ in linearity strengths. The difference in position amplitudes as an effect of coupling is reduced as the degree of the time derivative is systematically decreased from 1.0 to 0.9. The decrease in order increases the size of the limit cycle of the least non-linear oscillator but decreases those of the other two oscillators. It also increases the frequency while decreasing the non-linearity of all three oscillators.