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In this manuscript, we principally probe into a class of fractional-order tri-neuron neural networks incorporating delays. Making use of fixed point theorem, we prove the existence and uniqueness of solution to the fractional-order tri-neuron neural networks incorporating delays. By virtue of a suitable function, we prove the uniformly boundedness of the solution to the fractional-order tri-neuron neural networks incorporating delays. With the aid of the stability theory and bifurcation knowledge of fractional-order differential equation, a new delay-independent condition to guarantee the stability and creation of Hopf bifurcation of the fractional-order tri-neuron neural networks incorporating delays is established. Taking advantage of the mixed controller that contains state feedback and parameter perturbation, the stability region and the time of onset of Hopf bifurcation of the fractional-order trineuron neural networks incorporating delays are successfully controlled. Software simulation plots are displayed to illustrate the established key results. The obtained conclusions in this article have important theoretical significance in designing and controlling neural networks.

Dynamic Analysis and Bifurcation Study on Fractional-Order Tri-Neuron Neural Networks Incorporating Delays