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Discontinuity, Nonlinearity, and Complexity 2(3) (2013) 225--245 | DOI:10.5890/DNC.2013.08.002

Shasha Zheng; Xilin Fu

School of Management Science and Engineering, Shandong Normal University, Ji’nan, 250014, P.R. China

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Abstract

In this paper, we investigate the pulse phenomena for a class of impulsive dynamical systems. Some sufficient conditions that guarantee the absence or presence of pulse phenomena are obtained, without the boundeness requirement on impulse surfaces. Besides, we also utilize methods of the flow theory, focus on the dynamical behavior in the normal direction to the switching boundary and generalize several known results to apply to an important example. Then, we study the stability of a nontrivial solution in a class of functional differential equations with pulse phenomena by using the concept of quasistability and method of comparison.

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