Abstract
A new Lorenz-like chaotic system with varying parameter is proposed by adding a state feedback function. The structure of the new designed system is simple and has more complex dynamic behaviors. The chaos behavior of the new system is studied by theoretical analysis and numerical simulation. And the bifurcation diagram shows a chaos-cycle-chaos evolution when the new parameter changes. Then a new synchronization scheme by a single state variable drive is given based on the new system and a chaotic parameter modulation digital secure communication system is also constructed. The results of simulation demonstrate that the new proposed system could be well applied in secure communication. Otherwise, based on the new system, the encryption and decryption of image could be achieved also.
Highlights
With the development of the mobile, PC, cloud computing, the Internet of things, and wearable devices, the dataintensive science such as big data [1] has become the main topic of the technological reform
We show a new Lorenzlike system (3) with varying parameter; several conclusions can be gotten as follows: (i) b is a constant in Lorenz-like system (1) while it switches between d1 + d2 and d1 − d2 in system (3), so the new system’s structure has a slight difference with the Lorenz-like system (1) and it equals system (1) when θ ≤ 0 or θ ≫ 26.0678; (ii) new chaotic behaviors occur when θ change; (iii) the equilibrium points are not fixed for the reason of θ as Table 1 shows; and (iv) the Lyapunov exponent λL2 is apparently different
Compared with algorithms based on other chaotic systems in [29, 30], we can know that the correlation coefficients of ciphertext are nearly, but the time consumption is less for the proposed system. This comparison demonstrates that the proposed image encryption algorithm based on the new Lorenz-like system shows a good performance as well as algorithms based on other systems, and the efficiency is high for the reason of its simple structure
Summary
With the development of the mobile, PC, cloud computing, the Internet of things, and wearable devices, the dataintensive science such as big data [1] has become the main topic of the technological reform. Mei [21] proposed a new secure communication scheme based on uncertain time-delay chaos system. Other secure communication schemes based on fractional-order [23], time-delay [24], and Mathematical Problems in Engineering multiscroll [25] chaotic systems have been proposed . The more complicated structure of the chaotic systems, the better performance of the secure communications and cryptography. The new Lorenz-like chaotic system with varying parameter is designed based on the Lorenz-like system and analyzes its chaos characteristics theoretically. A synchronization scheme driven by a single state variable is achieved based on the new proposed system, and the chaotic parameter modulation digital secure communications system is constructed. The designed variable parameter chaotic system is applied to image encryption and a threechaotic-image encryption algorithm is proposed
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