一类推广的自治收敛定理的应用

主要研究一类带有快慢进展的结核病模型,利用再生矩阵法,通过推广的自治收敛定理证明该模型正平衡点的全局稳定性,并通过数值模拟验证其结果的正确性.从求证过程中可以看到,使用推广的自治收敛定理在解决全局稳定问题上有一定的规律可循,但在高维系统上也存在一定的局限性.

The Application of an Extended Autonomous Convergence Theorem

In this paper,we mainly focuse on a class of tuberculosis(TB)model with fast progressthe.With the help of the renewable matrix method,the global stability of the tuberculosis model is proved by an extended autonomous convergence theorem.And the accuracy of the model's conclusions are proved by numerical simulation.It can be seen that the autonomous convergence theorem to deal with the problem of global stability has certain rules to follow,but there has certain limitation in high-dimensional systems.