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This paper studies the problem on chaotic secure communication, and a new hyperchaotic system is included for the scheme design. Based on Lyapunov method and

Since the pioneer work of Fujisaka and Yamada in 1983 [

Hence, inspired by the above discussion, we try to propose the secure communication schemes based on a hyperchaotic system. The rest of the paper is organized as follows. In Section

Notations used in this paper are fairly standard. Let

First, based on the single-dimensional

Chaotic secure communication Scheme 1.

Thereinto, the master hyperchaotic system in transmitting terminal is designed by

The chaotic encrypted signal to be transmitted is defined by

The slave hyperchaotic system in receiving terminal is designed by

Define the tracking error variable as

The recovered signal is define by

Given any real vectors

Under the assumption of zero initial condition, the slave system (

In this section, based on Lyapunov method and LMI technology, the following theoretical results can be concluded.

For Scheme 1, if there exist scalars

Choose the following Lyapunov functional candidate:

Next, based on the multidimensional

Chaotic secure communication Scheme 2.

The master hyperchaotic system is constructed as

The slave system is constructed as follows:

Define the tracking error vector as

For chaotic secure communication Scheme 2, if there exist positive scalars

First choose the following Lyapunov function:

In this section, we include some examples to validate the effectiveness of two proposed secure communication schemes. The numerical simulation is with the step size of 0.001 second and the following initial parameters:

Time response of the state variable of the hyperchaotic system.

Time response of the disturbance input.

Time response of input signal and recovered signal based on Scheme 1.

Time response of the synchronization error variable based on Scheme 1.

Next, we consider secure communication Scheme 2. Based on Theorem

Time response of input signal and recovered signal based on Scheme 2.

Time response of the synchronization error variable based on Scheme 2.

From numerical simulation, we notice that the input signal in transmitting terminal can be restored precisely in receiving terminal at early stage; later when disturbance is added at 20th second, the synchronization error jitters in a small range, which satisfies the required

In this paper, a new hyperchaotic system is included for the secure communication scheme design in the case that disturbances exist. Based on Lyapunov method and

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was partially supported by the Young Scholars Project of Xihua University (01201419), the Open Research Subject of Key Laboratory of Signal and Information Processing of Sichuan Province (szjj2014-018), the Open Research Fund of Key Laboratory of Fluid and Power Machinery of Ministry of Education (SZjj2011-006), and the National Natural Science Foundation of China (61174058, 61134001).