A novel two-delayed tri-neuron neural network with an incomplete connection

In this paper, we propose a novel two-delayed tri-neuron neural network (NN) with no connection between the first and third neurons. Neural networks with incomplete connections offer a range of advantages, including improved efficiency, generalisation, interpretability, and biological plausibility, making them useful in various applications across different domains. Such kinds of NNs exist in some diseases, such as epilepsy, Alzheimer's, and schizophrenia, where the neuron's connections can be broken. Our NN is defined in two different forms: one with integer-order derivatives and another with Caputo fractional derivatives. The fundamental results of existence, uniqueness, and boundedness of the solution for the proposed NN are derived. We perform the bifurcation analysis along with the stability of the initial state of the fractional-order NN, considering self-connection delay and communication delay as bifurcation parameters, respectively. The proposed NN is numerically solved by using a recently proposed L1-predictor-corrector method with its error analysis. The theoretical proofs are verified through graphical simulations.