Dynamical transition and chaos for a five‐dimensional Lorenz model

Zhang, Dongpei; Deng, Dong

doi:10.1002/mma.7877

Cited by 3 publications

(1 citation statement)

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“…where σ, r, b, d are constant parameters. The dynamic properties and conditions of the new five-dimensional Lorenz model ( 6) were investigated in [22,25,[39][40][41]. They discussed in detail the numerical solutions, which included chaotic, periodic, and quasi-periodic responses.…”

Section: Integer Order Five-dimensional Lorenz Modelmentioning

confidence: 99%

Ultimate Boundedness and Finite Time Stability for a High Dimensional Fractional-Order Lorenz Model

et al. 2022

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In this paper, the global attractive set (GAS) and positive invariant set (PIS) of the five-dimensional Lorenz model with the fractional order derivative are studied. Using the Mittag-Leffler function and Lyapunov function method, the ultimate boundedness of the proposed system are estimated. An effective control strategy is also designed to achieve the finite time stability of this fractional chaotic system. The corresponding boundedness and control scheme are numerically verified to show the effectiveness of the theoretical analysis.

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Section: Integer Order Five-dimensional Lorenz Modelmentioning

confidence: 99%

Ultimate Boundedness and Finite Time Stability for a High Dimensional Fractional-Order Lorenz Model

et al. 2022

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First transition dynamics of reaction–diffusion equations with higher order nonlinearity

Şengül,

Tiryakioglu,

Yıldız Akıl

2024

Stud Appl Math

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In this study, the dynamics of a reaction–diffusion equation on a bounded interval at the first dynamic transition point is investigated. The main difference of this study from the existing ones in the dynamic transition literature is that in this work, no specific form of the nonlinear operator is assumed except that it is an analytic function of and . The linear operator is also assumed to be a general operator with sinusoidal eigenvectors. Moreover, we assume that there is a first transition as a real simple eigenvalue changes sign. With this general framework, we make a rigorous analysis of the dependence of the first transition dynamics on the coefficients of the Taylor expansion of the nonlinear operator. The main tool we use in this study is the center manifold reduction combined with the classification of the dynamic transition theory. This study is a generalization of a recent work where the nonlinear operator contains only low‐order (quadratic and cubic) nonlinearities. The current generalization requires certain technical difficulties such as the validity of the genericity conditions on the Taylor coefficients of the nonlinear operator and a bootstrapping argument using these genericity conditions. The results of this work can be generalized in various directions, which are discussed in the conclusions section.

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