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This paper deals with the dynamic behavior of the chaotic nonlinear time delay systems of general formẋ(t) = g(x(t), x(t -τ )). We carry out stability analysis to identify the parameter zone for which the system shows a stable equilibrium response. Through the bifurcation analysis, we establish that the system shows a stable limit cycle through supercritical Hopf bifurcation beyond certain values of delay and parameters. Next, a numerical simulation of the prototype system is used to show thatdoi:10.1186/s13662-019-2010-y fatcat:iwlivpa6xjaqfc4affkjne5d5i