A New 4D Piecewise Linear Multiscroll Chaotic System with Multistability and Its FPGA-Based Implementation

Due to the complex behavior of a multiscroll chaotic system, it is a good candidate for the secure communications. In this paper, by adding an additional variable to the modified Lorenz-type system, a new chaotic system that includes only linear and piecewise items but can generate 4n + 4 scroll chaotic attractors via choosing the various values of natural number n is proposed. Its dynamics including bifurcation, multistability, and symmetric coexisting attractors, as well as various chaotic and periodic behaviors, are analyzed by means of attraction basin, bifurcation diagram, dynamic map, phase portrait, Lyapunov exponent spectrum, and C0 complexity in detail. The mechanism of the occurrence for generating multiscroll chaotic attractors is presented. Finally, this multiscroll chaotic system is implemented by using the Altera Cyclone IV EP4CE10F17C8 FPGA. It is found that this FPGA-based design has an advantage of requiring less resources for 0% of the embedded multipliers and 0% of the PLLs of this FPGA are occupied.

An Image Encryption Algorithm Based on a New Memristor Chaotic System and DNA Variation

In this paper, a new memristor chaotic system is designed based on Chua’s memristor chaotic system. To get the complete picture of the brain of a three-dimensional chaotic attractor, red and blue 3D glasses is used to observe the chaotic attractor, and using Lyapunov exponent spectrum, SE complexity and C0 complexity to analyze dynamical characteristics of new memristor chaotic system. The results illustrate that the chaotic state of the new memristor chaotic system is distributed over a large parameter range, which shows that the new memristor chaotic system is more suitable for image encryption applications. To verify the image encryption application of the new memristor chaotic system, a novel image encryption algorithm is designed based on the new memristor chaotic system and DNA variation. The security performances of the designed algorithm indicate that the proposed algorithm can effectively encrypt image and has better security performance.

Detection Line Spectrum of Ship Radiated Noise Based on a New 3D Chaotic System

This paper proposes a new detection model of a weak signal based on a third-order chaotic system. Using a dynamic analysis tool, such as the Lyapunov exponent and the bifurcation diagram, variations of dynamic behavior can be observed, and the weak signal underwater can be picked up. In order to improve the observability of detection signals in the time domain and frequency domain, the spectral entropy complexity algorithm (SE) and C0 complexity algorithms are used to analyze and extract the weak signal. The experimental results show that the spectrum extraction based on the complexity algorithm can accurately reflect the dynamic characteristics of the detected signal. It provides the theoretical direction and experimental data support for the application of the chaotic system in the field of acoustic detection.

Design of 9-D global chaotic system and its application in secure communication

Purpose In this paper, a nine-dimensional chaotic system is designed and applied to secure communication. Design/methodology/approach Firstly, the equilibrium characteristics, dissipativity, bifurcation diagram and Lyapunov exponent spectrum are used to analyze the relevant characteristics of the proposed nine-dimensional chaotic system. In the analysis of Lyapunov exponential spectrum, when changing the linear parameters, the system shows two states, hyperchaos and chaos. For secure communication, there is a large secret key space. Secondly, C0 complexity and SEcomplexity of the system are analyzed, which shows that the system has sequences closer to random sequences. Findings The proposed nine-dimensional system has a large key space and more complex dynamic characteristics Originality/value The results show that the proposed nine-dimensional hyperchaotic system has excellent encryption capabilities and can play an important role in the field of secure communication.

Dynamics and Synchronization of the Fractional-Order Hyperchaotic System

The fractional-order Lorenz hyperchaotic system is solved as a discrete map by applying Adomian decomposition method (ADM). Dynamics of this system versus parameters are analyzed by LCEs, bifurcation diagrams, and SE and C0 complexity. Results show that this system has rich dynamical behaviors. Chaos and hyperchaos can be generated by decreasing the fractional derivative order q in this system. It also shows that the system is more complex when q takes smaller values. Moreover, coupled synchronization of fractional-order chaotic system is investigated theoretically. The synchronization performances with synchronization controller parameters and derivative order varying are analyzed. Synchronization and complexity of intermediate variables which generated by ADM are investigated. It shows that intermediate variables between the driving system and response system are synchronized and higher complexity values are found. It lays a technical foundation for secure communication applications of fractional-order chaotic systems.

CONVERGENCE OF C0 COMPLEXITY

In this paper, the convergence of C0 complexity is proved, some examples and applications are given to verify the results. From these examples, we can see that C0 complexity can also obtain robust results with short signals, and consequently it can be applied to the nonstationary signals, such as EEG signals.