Theory of Impulsive Differential Equations
Theory of Impulsive Differential Equations
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DOI：
10.1142/0906
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发表时间：
1989-05
期刊：
影响因子：
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通讯作者：
V. Lakshmikantham;D. Bainov;P. Simeonov
中科院分区：
文献类型：
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作者：
V. Lakshmikantham;D. Bainov;P. Simeonov
许多进化过程的特点是，在某些时刻，它们经历了突然的状态变化。这些过程受到短期扰动的影响，其持续时间与过程的持续时间相比可以忽略不计。因此，很自然地可以假定这些扰动是瞬时作用的，也就是说，以脉冲的形式。例如，已知许多生物现象，包括阈值、医学和生物学中的爆发节律模型、经济学中的最优控制模型、药物动力学和频率调制系统，确实表现出脉冲效应。因此，脉冲微分方程，即涉及脉冲效应的微分方程，作为几个真实的世界问题的观察到的演化现象的自然描述出现。
Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. These processes are subject to short-term perturbations whose duration is negligible in comparison with the duration of the process. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. It is known, for example, that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics and frequency modulated systems, do exhibit impulsive effects. Thus impulsive differential equations, that is, differential equations involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems.