Bifurcation and chaos in time delayed fractional order chaotic memfractor oscillator and its sliding mode synchronization with uncertainties

A novel chaotic memfractor oscillator with one unstable equilibriums is proposed. Various dynamic properties of the proposed system are derived and investigated to show the existence of chaotic oscillations. The fractional order time delayed model of the chaotic memfractor oscillator is derived considering time delay in the memcapacitor. Bifurcation of the time delayed system with its delay factor is investigated along with the parameter space bifurcation. A novel methodology for synchronizing identical time delayed systems with an uncertainty in the slave system is proposed and tested with the proposed time delayed fractional order chaotic memfractor oscillator.