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Period-Increasing Indicates Loss of Stability

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

E-mail Address: yangxs@hust.edu.cn

Corresponding author.

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and

Lei Wang

Department of Mathematics and Physics, Hefei University, Hefei 230601, P. R. China

E-mail Address: wanglei@hfuu.edu.cn

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https://doi.org/10.1142/S0218127419501591Cited by:0 (Source: Crossref)

Abstract

We first present a mathematical theory on period-increasing as an indicator of stability loss in a dynamical system of any dimension not less than two, and show that in two-dimensional autonomous ODEs, the period-increasing is closely associated with homoclinic or heteroclinic bifurcation. Then we demonstrate that the proposed period-increasing regime shift can occur in some ecological models.

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