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- W4200311797 abstract "This paper examines the dynamics of the exponential population growth system with mixed fractional Brownian motion. First, we establish some useful lemmas that provide powerful tools for studying the stochastic differential equations with mixed fractional Brownian motion. We offer some explicit expressions and numerical characteristics such as mathematical expectation and variance of the solutions of the exponential population growth system with mixed fractional Brownian motion. Second, we propose two sufficient and necessary conditions for the almost sure exponential stability and the <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mi>k</mi> </math> th moment exponential stability of the solution of the constant coefficient exponential population growth system with mixed fractional Brownian motion. Furthermore, we conduct some large deviation analysis of this mixed fractional population growth system. To the best of the authors’ knowledge, this is the first paper to investigate how the Hurst index affects the exponential stability and large deviations in the biological population system. It is interesting that the phenomenon of large deviations always occurs for addressed system when <math xmlns=http://www.w3.org/1998/Math/MathML id=M2> <mfenced open=( close=) separators=|> <mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </mrow> </mfenced> <mo><</mo> <mi>H</mi> <mo><</mo> <mn>1</mn> </math> . Moreover, several numerical simulations are reported to show the effectiveness of the proposed approach." @default.
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- W4200311797 date "2021-12-30" @default.
- W4200311797 modified "2023-10-14" @default.
- W4200311797 title "Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion" @default.
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- W4200311797 doi "https://doi.org/10.1155/2021/5079147" @default.
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