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<p>The notion of sequence shadowing property is introduced, and it is utilized as a tool for investigating the complexity of non-autonomous discrete systems (NADSs). In NADSs, the implication relationships among sequence asymptotic average shadowing property (SAASP), sequence average shadowing property (SASP), and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\underline{d}\)</EquationSource> <EquationSource Format="MATHML"><math> <munder> <mi>d</mi> <mo>̲</mo> </munder> </math></EquationSource> </InlineEquation>-sequence shadowing property (DSSP) are established, and an equivalent condition for pseudo-orbit shadowing property (PSP) is obtained. Furthermore, the relationship between SAASP and transitivity in NADSs is derived, and illustrative examples are provided to demonstrate the main findings. Moreover, the conditions under which an NADS with SAASP is Devaney chaotic are explored, and two criteria for Devaney chaos are obtained.</p>

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Sequence Asymptotic Average Shadowing Property, Transitivity, and Devaney Chaos in Non-autonomous Discrete Systems

  • 期刊论文

  • 发表日期：

    2025年4月8日

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  • Qigui Yang,
  • Jingmin Pi

摘要

The notion of sequence shadowing property is introduced, and it is utilized as a tool for investigating the complexity of non-autonomous discrete systems (NADSs). In NADSs, the implication relationships among sequence asymptotic average shadowing property (SAASP), sequence average shadowing property (SASP), and \(\underline{d}\) d ̲ -sequence shadowing property (DSSP) are established, and an equivalent condition for pseudo-orbit shadowing property (PSP) is obtained. Furthermore, the relationship between SAASP and transitivity in NADSs is derived, and illustrative examples are provided to demonstrate the main findings. Moreover, the conditions under which an NADS with SAASP is Devaney chaotic are explored, and two criteria for Devaney chaos are obtained.