On the existence of chaos for the fourth-order Moore–Gibson–Thompson equation

Lizama, Carlos; Murillo-Arcila, Marina

doi:10.1016/j.chaos.2023.114123

Chaos, Solitons & Fractals

2023

DOI: 10.1016/j.chaos.2023.114123

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On the existence of chaos for the fourth-order Moore–Gibson–Thompson equation

Carlos Lizama,

Marina Murillo-Arcila

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2024

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Relationships among Various Chaos for Linear Semiflows Indexed with Complex Sectors

He,

Liu,

Yin

et al. 2024

Mathematics

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In this paper, we investigate the relationships among point transitivity, topological transitivity, Li–Yorke chaos, and the existence of irregular vectors for a linear semiflow {Tt}t∈Δ indexed with a complex sector. We reveal the equivalence between topological transitivity and point transitivity for a linear semiflow {Tt}t∈Δ, especially in case the range of some operator Tt,t∈Δ is not dense. We also prove that Li–Yorke chaos is equivalent to the existence of a semi-irregular vector and that point transitivity is stronger than the existence of an irregular vector for any linear semiflow Ttt∈Δ. At last, unlike the conclusion for traditional linear dynamical systems, we show that there exists a Li–Yorke chaotic C0-semigroup Ttt∈Δ without irregular vectors. The results and proof methods presented in this paper demonstrate the differences in the dynamical behavior between linear semiflows {Tt}t∈Δ and traditional linear systems with the acting semigroup S=Z+ and S=R+.

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Relationships among Various Chaos for Linear Semiflows Indexed with Complex Sectors

He,

Liu,

Yin

et al. 2024

Mathematics

View full text Add to dashboard Cite

show abstract

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On the existence of chaos for the fourth-order Moore–Gibson–Thompson equation

Cited by 1 publication

References 25 publications

Relationships among Various Chaos for Linear Semiflows Indexed with Complex Sectors

Relationships among Various Chaos for Linear Semiflows Indexed with Complex Sectors

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