We studied local bifurcation and verified its occurrence after choosing the delay as a parameter of control in Zhou’s dynamical system with delayed feedback control. We investigated the normal form theory and the center manifold theorem in order to obtain explicit formulas to determine the stability of periodic solutions to the new\nsystem and study the extent of the stability of those periodic solutions and the direction of bifurcated periodic solutions. More than that, we did a numerical simulation to confirm the results that we obtained and presented through numerical analysis the periodic solution and stable solutions, and when the system returns again\nto the state of out of control

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