| Chaos is a non-periodic bounded dynamic behavior of deterministic nonlinear dynamical systems that are sensitive to initial values,and chaotic motion is a class of stochastic processes that appear in deterministic systems.The basic properties of chaos are boundedness,ergodicity,randomness,dimensionality,scalability,universality,and positive Lyapunov exponent,so it is highly reliable for information security.Nonlinear functions play an important role in constructing chaotic systems,and the hyperbolic property of hyperbolic sinusoidal functions is of great importance in constructing nonlinear circuits.State feedback controllers play a key role in constructing hyperchaotic systems.Compared with low-dimensional chaotic systems,the output sequences of hyperchaotic systems have higher randomness,key parameters,and more complex topology,so they can be applied in information encryption,secure communication,and chaotic radar.In this paper,we focus on the role of nonlinear functions on chaotic systems,the analysis of dynamical behavior of hyperchaotic systems,synchronization stability and applications in confidential communication in conjunction with the development of chaos theory in the field of information engineering:(1)The nonlinear functions contained in chaotic systems are of great interest.A new four-dimensional chaotic system with multi-winged attractors is proposed,which contains hyperbolic sinusoidal functions with nonlinearities that cause large changes in chaotic attractors.When the single parameter is changed,single,double and quadruple wing chaotic attractors are generated.The dynamical behavior of the chaotic system is analyzed,and the system is found to have coexisting attractors.An adaptive synchronization control method is derived,which can make the error system gradually stabilize at the origin and realize the chaotic synchronization with unknown parameters.A new electronic circuit for chaotic systems is designed and implemented in FPGA hardware to illustrate the accuracy and effectiveness of its existence.(2)A new five-dimensional hyperchaotic system with hyperchaotic attractors is proposed by introducing a state feedback controller to construct a hyperchaotic system.Its typical dynamical behavior is analyzed,and the existence of the hyperchaotic attractor is verified by MATLAB and Multisim simulations as well as circuit experiments.A staggered and adaptive synchronous control method for the system is implemented using Lyapunov stability theory.In this process,the synchronization speed in different cases is compared using two synchronization methods.The experimental results show that the staggered synchronization converges to the synchronized state in a shorter time.The hyperchaotic circuit is also implemented with basic electronic components to illustrate the correctness and reasonableness of the design.(3)A new confidential communication scheme for Lorenz-like hyperchaotic systems,capable of improving the security performance of transmitted signals,is introduced through an actively controlled synchronization method.The dynamical behavior of the hyperchaotic system is analyzed by MATLAB simulations.The circuit is designed by Multisim simulation to realize the encrypted transmission and decryption of signals,and the influence of input signal strength,frequency,and accuracy of electronic components on the confidential communication is analyzed.The circuit design is simple enough to perform experiments with hyper-chaotic synchronous,non-synchronous,and with or without modulated signals.The experiments of the analog electronic circuit using basic electronic components prove the effectiveness and accuracy of the design of hyperchaotic modulated secure communication.This secure communication circuit works stably,has low distortion,is easy to debug,and is convenient for mass production,and also has high bandwidth characteristics,which can significantly improve the security of information through the encryption of this secure communication.In conclusion,the research content of this paper has certain reference value for the analysis of the complex dynamic behavior of chaotic systems and provides theoretical support for the secure communication application of hyperchaotic systems. |
