关于 Bohr 混沌概念与不变测度的一些注记

关于玻尔混沌与双曲集的一个注记

A note on Bohr chaos and hyperbolic sets

研究动力系统中跟踪现象与玻尔混沌的关系，给出基于跟踪的玻尔混沌充分条件，结合跟踪引理得出关于玻尔混沌和双曲集的结果，突出双曲集结构性质。

主代数作用的Bohr混沌性与Riesz乘积测度

Bohr chaoticity of principal algebraic actions and Riesz product measures

该研究提出拓扑共轭不变的Bohr混沌性概念（强于正熵），证明正熵主代数$\u2124$作用均为Bohr混沌，且$d\ge2$时正熵主代数$\u2124^d$作用在可和同宿点存在条件下也满足该性质。

Remarks on the paper "Non-existence of Shilnikov chaos in continuous-time systems"

The present note refers to a result proposed in [Elhadj and Sprott, 2012], and shows that the Theorem therein is not correct. We explain that a proof of that Theorem cannot be given, as the statement is not correct, and we underline a mistake occurring in their proof. Since this note is supplementary to [Elhadj and Sprott, 2012], the reader should consult this paper for further explanations of the matter and the symbols used.

A remark on "Study of a Leslie-Gower-type tritrophic population model" [Chaos, Solitons and Fractals 14 (2002) 1275-1293]

In [Aziz-Alaoui, 2002] a three species ODE model, based on a modified Leslie-Gower scheme is investigated. It is shown that under certain restrictions on the parameter space, the model has bounded solutions for all positive initial conditions, which eventually enter an invariant attracting set. We show that this is not true. To the contrary, solutions to the model can blow up in finite time, even under the restrictions derived in [Aziz-Alaoui, 2002], if the initial data is large enough. We also prove similar results for the spatially extended system. We validate all of our results via numerica…

Periodic $p$-adic Gibbs measures of $q$-states Potts model on Cayley tree: The chaos implies the vastness of $p$-adic Gibbs measures

We study the set of $p$-adic Gibbs measures of the $q$-states Potts model on the Cayley tree of order three. We prove the vastness of the periodic $p$-adic Gibbs measures for such model by showing the chaotic behavior of the correspondence Potts--Bethe mapping over $\mathbb{Q}\_p$ for $p\equiv 1 \ (\rm{mod} \ 3)$. In fact, for $0 < |θ-1|\_p < |q|\_p^2 < 1$, there exists a subsystem that isometrically conjugate to the full shift on three symbols. Meanwhile, for $0 < |q|\_p^2 \leq |θ-1|\_p < |q|\_p < 1$, there exists a subsystem that isometrically conjugate to a subshift of finite type on $r$ sy…

测量Lorenz模型与Rössler模型中的混沌：储备池计算的保真度测试

Measuring chaos in the Lorenz and Rössler models: Fidelity tests for reservoir computing

本研究利用符号动力学方法表征Lorenz与Rössler混沌系统的混沌程度，验证了三种复杂度度量的有效性，并提出储备池计算保真度测试以检验模型对混沌特性的模拟能力。