[en] Uniform index is a conception that can describe the uniformity of a finite point set in a polyhedron, and is closely related to chaos. In order to study uniform index, the concept of contained uniform index is defined, which is similar to uniform index and has good mathematical properties. In this paper, we prove the convergence of the contained uniform index, and develop the base of proving the convergence of uniform index.

[en] In this article, we consider a system of autonomous inductively coupled Van der Pol generators. For two coupled generators, we establish the presence of metastable chaos, a strange non-chaotic attractor, and several stable limiting cycles. Areas of parametric dependence of different modes of synchronization are obtained

[en] Let $R_{r_0},R_{r_1}:{\mathbb{S}}^1⟶<!--\; ???\; -->{\mathbb{S}}^1$ be rotations on the unit circle ${\mathbb{S}}^1$ and define $f:{\mathrm{\Sigma <!--\; ??\; -->}}_2\times <!--\; ??\; -->{\mathbb{S}}^1⟶<!--\; ???\; -->{\mathrm{\Sigma <!--\; ??\; -->}}_2\times <!--\; ??\; -->{\mathbb{S}}^1$ as $$f(x,t)=(\mathrm{\sigma <!--\; ??\; -->}(x),R_{r_{x_1}}(t)),$$ for $x=x_1{x}_2\cdots <!--\; ???\; -->\in <!--\; ???\; -->{\mathrm{\Sigma <!--\; ??\; -->}}_2:=\{0,1{\}}^{\mathbb{N}}$, $t\in <!--\; ???\; -->{\mathbb{S}}^1$, where $\mathrm{\sigma <!--\; ??\; -->}:{\mathrm{\Sigma <!--\; ??\; -->}}_2⟶<!--\; ???\; -->{\mathrm{\Sigma <!--\; ??\; -->}}_2$ is the shift, and $r_0$ and $r_1$ are rotational angles. It is first proved that the system $({\mathrm{\Sigma <!--\; ??\; -->}}_2\times <!--\; ??\; -->{\mathbb{S}}^1,f)$ exhibits maximal distributional chaos for any $r_0,r_1\in <!--\; ???\; -->\mathbb{R}$ (no assumption of $r_0,r_1\in <!--\; ???\; -->\mathbb{R}\setminus <!--\; ???\; -->\mathbb{Q}$), generalizing Theorem 1 in Wu and Chen (Topol. Appl. 162:91–99, 2014). It is also obtained that $({\mathrm{\Sigma <!--\; ??\; -->}}_2\times <!--\; ??\; -->{\mathbb{S}}^1,f)$ is cofinitely sensitive and $({\stackrel{^<!--\; ^\; -->}{\mathcal{M}}}^1,{\stackrel{^<!--\; ^\; -->}{\mathcal{M}}}^1)$-sensitive and that $({\mathrm{\Sigma <!--\; ??\; -->}}_2\times <!--\; ??\; -->{\mathbb{S}}^1,f)$ is densely chaotic if and only if $r_1-<!--\; ???\; -->r_0\in <!--\; ???\; -->\mathbb{R}\setminus <!--\; ???\; -->\mathbb{Q}$.

[en] The relationship between some kinds of substitutions and admissible sequences is studied. Sufficient and necessary conditions for the admissibility of the sequences generated by non-constant length substitution and constant length substitution are investigated respectively

No abstract available

[en] This paper investigates the equal combination synchronization of a class of chaotic systems. The chaotic systems are assumed that only the output state variable is available and the output may be discontinuous state variable. By constructing proper observers, some novel criteria for the equal combination synchronization are proposed. The Lorenz chaotic system is taken as an example to demonstrate the efficiency of the proposed approach

[en] This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of “chaotic region” and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a “chaotic sea” for the Nosé-Hoover oscillator

[en] Anti-synchronization between different hyperchaotic systems is presented using Lorenz and Liu systems. When the parameters of two systems are known, one can use active synchronization. When the parameters are unknown or uncertain, the adaptive synchronization is applied. The simulation results verify the effectiveness of the proposed two schemes for anti-synchronization between different hyperchaotic systems

[en] We study the dynamics of Laplacian-type coupling induced by logistic family $f_{\mu }\left(x\right)=\mu x(1-x)$, where $\mu \in [0,4]$, on a periodic lattice, that is the dynamics of maps of the form $F(x,y)=((1-\epsilon )f_{\mu }\left(x\right)+\epsilon f_{\mu }\left(y\right),(1-\epsilon )f_{\mu }\left(y\right)+\epsilon f_{\mu }\left(x\right))$ where $\epsilon >0$ determines strength of coupling. Our main objective is to analyze the structure of attractors in such systems and especially detect invariant regions with nontrivial dynamics outside the diagonal. In analytical way, we detect some regions of parameters for which a horseshoe is present; and using simulations global attractors and invariant sets are depicted.

[en] Based on the generalized Lorenz system, a conjugate Lorenz-type system is introduced, which contains three different chaotic attractors, i.e., the conjugate Lorenz attractor, the conjugate Chen attractor and the conjugate Lue attractor. These new attractors are conjugate, respectively, to the Lorenz attractor, the Chen attractor and the Lue attractor in an algebraic sense. The conjugate attractors may be helpful for finally revealing the geometric structure of the Lorenz attractor.