This work is devoted to study the application of contraction mapping theorem to analyze a class of n -dimensional neural network model consisting of multiple delays with self-feedback and studying the dynamic behaviour of the system and obtain stability condition under the effect of time delay. Some novel and sufficient conditions are derived to ensure the existence and uniqueness of the solution and the global stability of the considered system at the same time under delay effect. Global asymptotic stability is discussed by constructing suitable Lyapunov functional. To check the dynamics of system, Local Hopf bifurcation analysis has also been done when the number of neurons reduces to two followed by finding the direction and stability of Hopf bifurcation. In the end, the analytical findings are validated using two numerical examples.
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