论文标题
解决方案对某些非自治多维非线性系统的稳定性和界限
Stability and Boundedness of Solutions to Some Non-autonomous Multidimensional Nonlinear Systems
论文作者
论文摘要
评估具有时间依赖性和非周期系数的多维非线性系统的界限/稳定性是一个重要的问题，在各种应用领域，尚无足够的分辨率。大多数已知技术在该领域提供了计算密集型和保守的稳定性标准，并且经常无法估计解决方案对相应系统的界限/稳定性区域。最近，我们概述了一种新方法，该方法基于对从上述解决方案规范到原始系统的上述时间历史界的标量辅助方程的分析。本文开发了一种新型技术，以修改形式施放辅助方程，该方程扩展了应用域并减少了我们先前方法的计算篮。因此，我们为某些具有非周期性时间依赖性系数的多维非线性系统开发了更一般的界限/稳定性标准和估计的捕获/稳定区域，这些系统在各个应用域中很常见。这让我们在目标模拟中评估某些多维，非线性和时变系统的界限/稳定性程度，这些系统与我们先前的技术相关。
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the known techniques provide computationally intensive and conservative stability criteria in this field and frequently fail to estimate the regions of boundedness/stability of solutions to the corresponding systems. Recently, we outlined a new approach to this problem which is based on the analysis of solutions to a scalar auxiliary equation bounded from the above time histories of the norms of solutions to the original system. This paper develops a novel technique casting the auxiliary equation in a modified form which extends the application domain and reduces the computational hamper of our prior approach. Consequently, we developed more general boundedness/stability criteria and estimated trapping/stability regions for some multidimensional nonlinear systems with nonperiodic time-dependent coefficients that are common in various application domains. This let us to assess in target simulations the extent of boundedness/stability of some multidimensional, nonlinear and time-varying systems which were intractable with our prior technique.
