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Keywords:
exponential stability; neural network; nonconformable derivative
exponential stability; neural network; nonconformable derivative
Summary:
This work focuses on a particular type of Hopfield neural network that generalizes classical fractional derivatives and is distinguished by nonconformable fractional derivatives. The main goal is to determine the basic characteristics of these networks, such as the circumstances under which equilibrium points are present and distinct. By demonstrating the exponential stability of the network, we further investigate its behavior and rigorously deduce these criteria. This is accomplished by constructing a Lyapunov function, a potent instrument frequently used in stability studies. In addition to verifying the obtained stability constraints, the theoretical conclusions are supported by comprehensive numerical simulations that show the dynamics of the neural network in a variety of circumstances. These simulations provide specific illustrations of how the network reacts to various parameter combinations and inputs. Overall, this work contributes to the understanding of neural networks with fractional-order dynamics, offering insights into their mathematical properties and potential applications in areas requiring robust and stable systems.
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