Accelerated convergent zeroing neurodynamics models for solving multi-linear systems with M-tensors

As a special type of neurodynamic methodology dedicated to finding zeros of equations, zeroing neurodynamics has shown a powerful ability in solving challenging online time-varying problems. Multi-linear systems, on the other hand, are a type of tensor equations with a wide range of applications. In this paper, a zeroing neurodynamics approach for solving multi-linear systems with M -tensors is proposed along with three specific accelerated finite-time convergent zeroing neurodynamics models, which breaks the limitations of a recently presented neural network approach termed continuous time neural network. Activation functions available in constructing zeroing neurodynamics models for solving multi-linear systems with M -tensors are also investigated in the rest of the paper. Theoretical analyses prove that the proposed zeroing neurodynamics approach is stable in the sense of Lyapunov stability theory and the proposed models converge to the theoretical solution in finite time. Finally, computer simulations are provided to substantiate the efficacy and superiority of the proposed zeroing neurodynamics models for solving multi-linear systems with M -tensors.