Fractional-order complex-valued neural networks: Stability results, numerical simulations and application to game-theoretical decision making

In this article, we first address the quasi-uniform stability results with constant-time delay in the context of fractional-order complex-valued neural networks. We provide the necessary criteria for the quasi-uniform stability of fractional-order complex-valued neural networks with known inequalities, such as Hölder's inequality, Cauchy–Schwartz inequality and Gronwall inequality. Nevertheless, no study has been written explaining the quasi-uniform stability of time-delayed fractional-order complex-valued neural networks. So, it is important and difficult to determine the sufficient criteria for such fractional-order complex-valued neural networks. At some point, a computational illustration is presented in order to validate the possible outcomes. Thereafter, we propose an algorithm for predicting enemy behavior in a game using fractional-order complex-valued neural networks. As an application, we focus on utilizing fractional-order complex-valued neural networks to predict enemy behavior in a turn-based strategy game. The fractional-order complex-valued neural network model is trained on pertinent data consisting of player health, distance to the enemy, and corresponding enemy actions. The network architecture includes an input layer, a hidden layer with complex-valued activations and weights, and an output layer predicting the probability of enemy actions. A numerical example is presented to illustrate the calculation of the probability of the enemy performing the action 'Attack' given a specific game state and trained fractional-order complex-valued neural network parameters. Moreover, this article demonstrates the effectiveness of fractional-order complex-valued neural networks in modeling complex game dynamics and predicting enemy behavior, contributing to advancements in strategic decision-making in games.