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We investigated the effects of variation in the non-integer order of a fractional differential equation modeling activated enzyme molecules in brain wave. The dynamical changes in the system trajectories in both the chaotic and the periodic regimes of an existing second order differential equation model are numerically examined when the orders of the biological system are assigned non-integer values. The simulation showed that the dynamics of the system can be altered through the order of the derivatives. In particular, the integer-order system can be driven from chaotic oscillation into periodic state by adopting an appropriate non-integer orders when the system is associated with innate memory.

Chaotic and Periodic Behavior in a Fractional-order Biological System