Effect of fractional-order, time-delay and noisy parameter on slow-passage phenomenon in a nonlinear oscillator

In this paper, we report the effect of fractional order, time delay and noisy parameter on slow passage phenomenon in a nonlinear oscillator. We consider a second order LCR based nonlinear electronic circuit with a time varying resistor and use sinusoidal modulation on the resistor to change the resistance value. The time dependent parameter of a dynamical system causes slow passage effect which leads to bifurcation delay in the system dynamics and leaving the actual bifurcation point unpredictable. We find that the fractional order of the system significantly changes the magnitude of bifurcation delay and brings the system to oscillatory state. While the time delay in dynamical systems destroys the stable steady state leading it to oscillatory state. We study both these fractional order and time delay and their combined effect on the slow passage effect. We have also included the noise with the sinusoidal periodic modulation on the resistor to understand the effect of noise on the slow passage effect and found that the noise enhances the oscillatory behaviour of the system.