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Noise expresses exponential growth under regime switching

Hu, Guangda and Liu, Mingzhu and Mao, Xuerong and Song, Minghui, National Natural Science Foundation of China (Funder), University of Science and Technology, Beijing (Funder), Harbin Institute of Technology (Funder) (2009) Noise expresses exponential growth under regime switching. Systems and Control Letters, 58 (9). pp. 691-699. ISSN 0167-6911

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Abstract

Consider a given system under regime switching whose solution grows at most polynomially, and suppose that the system is subject to environmental noise in some regimes. Can the regime switching and the environmental noise work together to make the system change signicantly? The answer is yes. In this paper, we will show that the regime switching and the environmental noise will make the original system whose solution grows at most polynomially become a new system whose solution will grow exponentially. In other words, we reveal that the regime switching and the environmental noise will exppress the exponential growth.