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Noise suppresses exponential growth under regime switching

Authors
Publisher
Elsevier
Publication Date
Keywords
  • Mathematics
Disciplines
  • Ecology
  • Geography

Abstract

Consider a given system under regime switching whose solution grows expo- nentially, 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 exponentially become a new system whose solutions will grow at most polynomially. In other words, we reveal that the regime switching and the environmental noise will suppress the exponential growth.

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