A “three sections, three periods” mechanism is proposed to discuss the formation and transformation of confined species and its effects on catalyst deactivation and product selectivity.

We study constructive generalized synchronization (GS) for bidirectional discrete arrays of difference systems (BDADSs). The result provides a general representation of GS in BDADSs. Numerical simulations are presented to show the effectiveness of the theoretical results.

Recently chaos-based encryption has been obtained more and more attention. Chaotic systems without equilibria may be suitable to be used to design pseudorandom number generators (PRNGs) because there does not exist corresponding chaos criterion theorem on such systems. This paper proposes two propositions on 4-dimensional systems without equilibria. Using one of the propositions introduces a chaotic system without equilibria. Using this system and the generalized chaos synchronization (GCS) theorem constructs an 8-dimensional discrete generalized chaos synchronization (8DBDGCS) system. Using the 8DBDGCS system designs a 216-word chaotic PRNG. Simulation results show that there are no significant correlations between the key stream and the perturbed key streams generated via the 216-word chaotic PRNG. The key space of the chaotic PRNG is larger than 21275. As an application, the chaotic PRNG is used with an avalanche-encryption scheme to encrypt an RGB image. The results demonstrate that the chaotic PRNG is able to generate the avalanche effects which are similar to those generated via ideal chaotic PRNGs.

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