A new class of tensors called \(\mathcal {K}\mathcal {S}\)-tensors, which is a subset of non-singular \(\mathcal {P}\)-tensors and generalization of \({\mathscr{H}}^{+}\)-tensors, is proposed. It is proved that the system of \(\mathcal {K}\mathcal {S}\)-tensor equations always has a unique positive solution for any positive right-hand side by proposing a positive increasing map. Two approaches based on dynamical system are presented to find the unique positive solution. The theoretical analysis results show that the convergence of the proposed models is guaranteed, and numerical examples further illustrate that the given models are feasible and effective in finding the positive solution of \(\mathcal {K}\mathcal {S}\)-tensor equations.

一类新的张量称为\（\ mathcal {K} \ mathcal {S} \）- tensors，它是非奇异\（\ mathcal {P} \）-张量和\（{\ mathscr提出了{H}} ^ {+} \）-张量。通过提出一个正递增映射，证明了（{mathcal {K} \ mathcal {S} \）-张量方程组对于任何正右手边总是具有唯一的正解。提出了两种基于动力学系统的方法来寻找唯一的正解。理论分析结果表明，所提出模型的收敛性是有保证的，数值算例进一步表明，所给出的模型对于找到\（\ mathcal {K} \ mathcal {S} \）的正解是可行和有效的。张量方程。