Abstract
This paper proposes a class of time-delay fractional complex Lu¨ system and utilizes the adomian decomposition algorithm to study the dynamics of the system. Firstly, the time chaotic attractor, coexistence attractor and parameter space are studied. The bifurcation diagram and complexity are used to analyze the dynamic characteristics of the system. Secondly, the definition of modified fractional projective difference function synchronization (MFPDFS) is introduced. The corresponding synchronous controller is designed to realize the MFPDFS of the time-delay fractional complex Lu¨ system. Thirdly, based on the background of wireless speech communication system (WSCs), the MFPDFS controller is used to realize the secure speech transmission. Finally, the effectiveness of the controller is verified by numerical simulation. The signal-noise ratio (SNR) analysis of speech transmission is given. The performance of secure communication is verified by numerical simulation.
Highlights
The proposed secure communication scheme based on the time-delay fractional complex Lü system has the following advantages: (1) The fractional complex chaotic system considers the fractional domain and combines the complex number domain, and the robustness of the system can be improved by increasing the complex scale factor; (2) In our communication scheme, we use an modified fractional projective difference function synchronization (MFPDFS) controller to ensure that the receiving end signal is equal to the addition of the plaintext signal and the fractional complex chaotic signal; (3) In the transmission process, one of the five channels is randomly selected, and the possibility of an eavesdropper to obtain the original information signal is very small, which greatly improves the security of communication
The dynamic characteristics of the system are analyzed by a bifurcation diagram and complexity algorithm
It is concluded that the complexity of a fractional order complex chaotic system decreases with the increase of fractional order in a certain range, and remains high with the change of parameters in a certain range
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Li et al [7] proposed a communication scheme for signal encryption and decryption, and designed an adaptive sliding mode controller to realize the synchronization stage between the encryption systems. From the symmetry of the system, the stability of the equilibrium point, the bifurcation and the differential order when the system parameters change, the chaotic characteristics of the system were studied, and the feedback control technology was used to design the controller to give the analysis of the function projective synchronization scheme of the fractional complex T system. In 2014, Jiang proposed a fractional-order complex Lü system and studied its chaotic characteristics including the symmetry of the system, the stability of the equilibrium point and the bifurcation of the differential order They used the method of active control and state observer to realize its anti-synchronization [23].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
