In this paper time-delay effects on the master-slave synchronization scheme are investigated. Sufficient conditions for master-slave synchronization of Lur'e systems are presented for a known time-delay in the master and slave systems. A delay-dependent synchronization criterion is given based upon a new Lyapunov-Krasovskii function. The derived criterion is a sufficient condition for global asymptotic stability of the error system, expressed by means of a matrix inequality. The feedback matrix follows from solving a nonlinear optimization problem. The method is illustrated for the synchronization of Chua's circuits, 5-scroll attractors and hyperchaotic attractors.

In this paper a new family of scroll grid attractors is presented. These families are classified into three called 1D-, 2D-and 3D-grid scroll attractors depending on the location of the equilibrium points in state space. The scrolls generated from 1D-, 2D-and 3D-grid scroll attractors are located around the equilibrium points on a line, on a plane or in 3D, respectively. Due to the generalization of the nonlinear characteristics, it is possible to increase the number of scrolls in all state variable directions. A number of strange attractors from the scroll grid attractor families are presented. They have been experimentally verified using current feedback opamps. Also Lur'e representations are given for the scroll grid attractor families.

In this paper, a novel true random bit generator (TRBG) based on a double-scroll attractor is proposed. The double-scroll attractor is obtained from a simple model which is qualitatively similar to Chua's circuit. In order to face the challenge of using the proposed TRBG in cryptography, the proposed TRBG is subjected to statistical tests which are the well-known Federal Information Processing Standards-140-1 and Diehard test suite in the area of cryptography. The proposed TRBG successfully passes all these tests and can be implemented in integrated circuits.

Abstract-In this letter we present an experimental confirmation of 3-and 5-scroll attractors from a generalized Chua's circuit. The generalized Chua's circuit introduced by Suykens, Huang, and Chua makes use of a piecewise linear characteristic with multiple breakpoints leading to a more complete family of -scroll attractors than -double scroll attractors, with a natural number.

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