Quasi-projective synchronization of discrete-time tempered fractional-order neural networks with time delays

Due to the finite lifespan of particles and constraints imposed by physical space, tempered fractional calculus has attracted increasing attention. This paper focuses on discrete-time tempered fractional neural networks (DTFNNs) with time delays and investigates their quasi-projective synchronization. By employing discrete convolution techniques and the discrete Laplace transform of tempered fractional operators, a fractional difference inequality is derived. Combining inequality methods with the Lyapunov function approach, easily verifiable sufficient conditions are established to guarantee synchronization of the proposed neural networks under a designed adaptive controller. Finally, numerical simulations are presented to validate the effectiveness and applicability of the theoretical results.