Synchronizing spatio-temporal chaos with imperfect models: a stochastic surface growth picture

Faceted patterns and anomalous surface roughening driven by long-range temporally correlated noise

We investigate Kardar-Parisi-Zhang (KPZ) surface growth in the presence of power-law temporally correlated noise. By means of extensive numerical simulations of models in the KPZ universality class we find that, as the noise correlator index increases above some threshold value, the surface exhibits anomalous kinetic roughening of the type described by the generic scaling theory of Ramasco et al. [Phys. Rev. Lett. 84, 2199 (2000)PRLTAO0031-900710.1103/PhysRevLett.84.2199]. Remarkably, as the driving noise temporal correlations increase, the surface develops a characteristic pattern of macroscopic facets that completely dominates the dynamics in the long time limit. We argue that standard scaling fails to capture the behavior of KPZ subject to long-range temporally correlated noise. These phenomena are not not described by the existing theoretical approaches, including renormalization group and self-consistent approaches.

Generation and dynamics analysis of N-scrolls existence in new translation-type chaotic systems

In this paper, we propose two kinds of translation type chaotic systems for creating 2 N + 1-and 2(N + 1)-scrolls chaotic attractors from a simple three-dimensional system, which are named the translation-2 chaotic system (a₁₂a₂₁ < 0) and the translation-3 chaotic system (a₁₂a₂₁ > 0). We also propose the successful design criterion for constructing 2 N + 1-and 2(N + 1)-scrolls, respectively. Then, the dynamics property of the translation-2 chaotic system is studied in detail. MATLAB simulation results show that very sophisticated dynamical behaviors and unique chaotic behaviors of the system. Finally, the definition and criterion of multi-scroll attractors for the translation-3 chaotic system is obtained. Three representative examples are shown in some classical chaotic systems that can be equally obtained via the set parameters of the translation type chaotic system. Furthermore, we show that the translation type chaotic systems have similar but topologically non-equivalent chaotic attractors, and they are the three-dimensional ordinary differential equations.

Generation of 2N + 1-scroll existence in new three-dimensional chaos systems

We propose a systematic methodology for creating 2N + 1-scroll chaotic attractors from a simple three-dimensional system, which is named as the translation chaotic system. It satisfies the condition a12a21 = 0, while the Chua system satisfies a12a21 > 0. In this paper, we also propose a successful (an effective) design and an analytical approach for constructing 2N + 1-scrolls, the translation transformation principle. Also, the dynamics properties of the system are studied in detail. MATLAB simulation results show very sophisticated dynamical behaviors and unique chaotic behaviors of the system. It provides a new approach for 2N + 1-scroll attractors. Finally, to explore the potential use in technological applications, a novel block circuit diagram is also designed for the hardware implementation of 1-, 3-, 5-, and 7-scroll attractors via switching the switches. Translation chaotic system has the merit of convenience and high sensitivity to initial values, emerging potentials in future engineering chaos design.