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We propose a three-dimensional autonomous nonlinear system,called the general T system, which has potential applications in secure communicationsand the electronic circuit. For the general T system with delayed feedback, regarding thedelay as bifurcation parameter, we investigate the effect of the time delay on its dynamics. We determine conditions for the existence of the Hopf bifurcations and analyze their directionand stability. Also, the fractional order general T-system is proposed and analyzed. We provide some numerical simulations, where the chaos attractor and the dynamics ofthe Lyapunov coefficients are taken into consideration. The effectiveness of the chaoticcontrol and synchronization on schemes for the new fractional order chaotic system areverified by numerical simulations.

Integer and Fractional General T-System and Its Application to Control Chaos and Synchronization