Dynamical Characterization Of Time-delay Chaotic Systems And Its Applications

The rapid development of information technology not only brings convenience to our daily life,but leads to major security issues such as information leakage during the dissemination of important information.Therefore,higher requirements are put forward for information security and confidentiality technology.Chaos widely exists in our life,and the initial condition sensitivity and inherent randomness of chaotic systems make chaotic signals difficult to be cracked.That is,chaotic signals generated by chaotic systems have a natural invisibility,which means that chaotic dynamic systems have a very broad development prospect in the application and research of secure communication fields.However,compared with finite dimensional chaotic systems represented by ordinary differential equations(ODE),the dynamic behavior of infinite dimensional chaotic systems represented by delay differential equations(DDE)is more complex and diverse.That is,chaotic signals generated by time-delay chaotic systems represented by DDEs are more difficult to be deciphered.Besides,there is less analysis and research on time-delay chaotic systems.Therefore,this thesis mainly focuses on dynamic behavior analysis,circuit implementation principles,and applications of the proposed time-delay chaotic systems.The main work of this thesis are as follows:(1)Chaotic systems with hidden multi-stability are more sensitive to initial conditions and are also a hot topic of current research,therefore,a time-delay chaotic system with hidden multi-stability is proposed.According to the calculation,the system has line equilibrium points,that is,the system has hidden attractors.By analyzing the dynamical characteristics of the proposed system,special nonlinear phenomena,such as multi-state coexistence of attractors,can be observed,which verifies that the proposed time-delay chaotic system has multi-stability.Besides,the approximate entropy of the chaotic pseudo-random sequences generated by this system is calculated to be greater than the that of other time-delay chaotic systems.This further indicates that the time-delay chaotic system has stronger randomness.(2)In order to verify the superiority of infinite dimensional time-delay chaotic systems described using DDE compared to finite dimensional chaotic systems described using ODE,a time-delay hyperchaotic system is proposed.Based on a 4D ODE described chaotic system,the system is transformed into a DDE described time-delay chaotic system by introducing two delay parameters into its two state variables.By comparing changes of the system before and after the introduction of delay parameters,it is found that the value of Lyapunov exponent(LE)of the system changes from one positive to multiple positive,and the coexistence characteristics of the system become more obvious.Bseides,the results of the Multisim simulation circuit are similar with those of the numerical simulation.Finally,a digital image encryption algorithm based on this system is proposed by introducing a hashing algorithm.The proposed encryption algorithm has good key sensitivity and plaintext sensitivity to external interference,and can effectively achieve plaintext image encryption.In summary,this further illustrates the good randomness of this system and advantages of the encryption algorithm.(3)In order to prove the authenticity of time-delay chaotic systems,a time-delay chaotic system with simple structure but rich dynamic behavior was constructed.The system not only has multi-stability,but also generates phase diagrams that can be distributed in one-dimensional lines,two-dimensional lattices,and three-dimensional meshes,which means the existence of multi-directional attractors.Moreover,the rare transient chaos phenomenon that exists in this system.In addition,a hardware simulation circuit of this time-delay chaotic system is built on a breadboard using common circuit components to further verify the feasibility of the system.Finally,experiments on spectral entropy complexity and image encryption performance verify the superiority of this system.