Modeling,Circuit Implementation And Synchronization Of Conditionally Symmetric Chaotic And Hyperchaotic Systems

With the development of chaos theory,chaotic secure communication also extends to higher levels.In order to improve confidentiality and applicability,it's necessary to obtain chaotic signal sources with higher complexity,stronger anti-interference and easier control.Hyperchaotic systems are folded and reversed in phase space,showing greater instability,are considered to have higher dynamic complexity.On the other hand,memristor as an emerging basic circuit element,has been being paid more and more attention especially after the development of physical devices.Memristors can provide non-linear feedback for the construction of chaotic systems.By the aid of memristors,it is possible to construct chaotic systems with high complexity and even multistability.The purpose of this study is to construct conditional symmetric hyperchaotic systems and conditional symmetric chaotic systems based on memristors.Through system modeling,circuit design,and synchronization analysis,reveal the dynamic characteristics of the system and lay the foundation for application.The main work done in this paper includes:A conditional symmetric memristive chaotic system is proposed,and the evolution law of its polarity regulation and amplitude frequency control is explored.Based on the principle of conditional symmetry,a chaotic system model with only a single linear term is studied,and a conditional symmetric memristive chaotic system is constructed by introducing a nonlinear function.Based on the analysis of the equilibrium stability and dissipation,basic dynamic characteristics of the system are further analyzed.Through analysis,it is found that memristor doesn't change the amplitude of its internal variables,but control the amplitude and frequency of other variables.The initial conditions analysis reveals multistability property of the system.A simulation platform for conditional symmetric memristive system is constructed by analog unit circuit to verify the physical properties.Based on asymmetric and symmetric hyperchaotic system,two models of conditional symmetric hyperchaos are constructed,whose unique dynamic behavior are studied.By conditional symmetric transformation of chaotic systems,a symmetric hyperchaotic system with polarity control and bias control and an asymmetric hyperchaotic system with polarity control,offset boosting control,and amplitude frequency control are constructed.The effects of system parameters and initial conditions on the dynamic evolution of the system are analyzed.Theoretical derivation or numerical simulation is performed through offset boosting parameters in non-bifurcation parameters,amplitude-frequency control caused by special bifurcation parameters and polarity control under the influence of initial conditions.Discrete modeling of continuous system equations using a microcontroller circuit platform to realize conditional symmetric hyperchaotic systems by digital method.Synchronization of conditional symmetric chaotic systems is studied,and the linear feedback synchronization is realized.Based on the principle of linear feedback synchronization,the application conditions and scope of the synchronization method are studied.Based on system analysis,a new synchronization model is constructed,and a new synchronization error system is established.The synchronization effect of the system is studied.The synchronization effect of system with polarity control,offset boosting control,and amplitude frequency control is studied to give different solutions.